In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale in...In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.展开更多
Experts question why cities, which are supposedly built for citizens, fail to addresstheir social needs. Everyday life is challenging in our cities, especially because public spaceshave generally been arranged and des...Experts question why cities, which are supposedly built for citizens, fail to addresstheir social needs. Everyday life is challenging in our cities, especially because public spaceshave generally been arranged and designed by considering the physical environment and withoutconsideration for how these spaces should facilitate human interactions. This paper identifies“in-between spaces” as key scenarios for addressing this issue. These spaces offer the opportunity to feel comfortable and safe, foster a sense of community, and facilitate connections.Little has been written about these spaces and, particularly, their characteristics. Therefore,the objective of this study is to provide a more in-depth understanding of in-between spaces byexamining literature on such spaces throughout city history.The results underscore the threshold character as the primary feature of in-between spacesand define various types of in-between spaces depending on their position within the gradientbetween public and private domains. The analysis also identified recurring characteristics, suchas presence of reproductive labor, vegetation, or amenities, tendency to be programmed or unprogrammed within interior or exterior spaces and establishes relationships between these characteristics. Furthermore, the results suggest that the values promoted by these spaces and theirrecurring features can offer solutions to regenerate cities.展开更多
This study reflects on the impact that the neighborhoods’in-between spaces have on:spatial perception,social interaction,and security.These sites,characterized by their abandonment and deterioration,can also be seen ...This study reflects on the impact that the neighborhoods’in-between spaces have on:spatial perception,social interaction,and security.These sites,characterized by their abandonment and deterioration,can also be seen as crucial spaces of opportunity for cities,in the architectural,urban and landscape research.This paper aims to analyze the sociospatial relationships in the neighborhoods’in-between spaces and examine the impact of inbetween space configuration on urban habitability.The investigation draws on a survey of perception to residents about the requirements for a suitable social interaction in these spaces.This study was developed in a neighborhood in the city periphery,characterized by their social dynamics and location in a nature conservation area.The findings indicate that the appropriation process,activities,and collective practices are dependent on the spatial legibility,in this case when this increases,gives rise to improve the habitability and the rehabilitation of the in-between space.Furthermore,the lack of design on in-between spaces substantially affects the use of these spaces and the social interaction among residents.展开更多
This research examines the impact of in-between space configuration on users'social practices.The effects of different degrees of permeability of these spaces on the social interactions of the inhabitants are also...This research examines the impact of in-between space configuration on users'social practices.The effects of different degrees of permeability of these spaces on the social interactions of the inhabitants are also analyzed.This research is based on a comparative approach using space syntax analysis and snapshot observations on four mass housing neighborhoods in Serif,Algeria.The neighborhoods are selected according to their degree of permeability,location in the city,realization period,and syntax measures from integrated to segregated.The activity patterns of two-week days for each study case are observed and recorded.Correlation results of observed social activities and syntactic measures demonstrate that spatial configuration affects people's use of in-between spaces.Moreover,connectivity and clustering coefficients are revealed to be important indicators of social activities.Previous urban studies argued that integrated spaces are mostly used by people.However,social interaction in the studied cases increases in the least connected areas,adjoining spaces to the buildings,and most closed spaces.This research finds that social activities are dependent on the degree of permeability,which when low,gives rise to increased social interaction and activities.展开更多
Depolarizing behavior is commonly observed in most natural samples.For this reason,optical tools measuring the differences in depolarization response among spatially separated structures are highly useful in a wide ra...Depolarizing behavior is commonly observed in most natural samples.For this reason,optical tools measuring the differences in depolarization response among spatially separated structures are highly useful in a wide range of imaging applications for enhanced visualization of structures,target identification,etc.One commonly used tool for depolarizing discrimination is the so-called depolarizing spaces.In this article,we exploit the combined use of two depolarizing spaces,the indices of polarization purity(IPP)and polarizance–reflection–transformation(PRT)spaces,to improve the capability of optical systems to identify polarization–anisotropy depolarizers.The potential of these spaces to discriminate among different depolarizers is first studied from a series of simulations by incoherently adding diattenuations or retarders,with some control parameters emulating samples in nature.The simulated results demonstrate that the proposed methods are capable of increasing differences among depolarizers beyond other well-known techniques.Experimentally,validation is provided by conducting diverse phantom experiments of easy interpretation and mimicking the stated simulations.As a useful application of our approach,we developed a model able to retrieve intrinsic microscopic information of samples from macroscopic polarimetric measurements.The proposed methods enable non-invasive,straightforward,macroscopic characterization of depolarizing samples,and may be of interest for enhanced visualization of samples in multiple imaging scenarios.展开更多
In the context of rural revitalization,the landscape design of public spaces in Enshi Xiaomaopoying Village presents both new opportunities and challenges.This study explores the significance of integrating regional c...In the context of rural revitalization,the landscape design of public spaces in Enshi Xiaomaopoying Village presents both new opportunities and challenges.This study explores the significance of integrating regional culture into rural public spaces.Field research has been conducted to assess the current utilization of regional culture in the public spaces of Xiaomaopoying Village.Subsequently,design optimization strategies are analyzed and proposed.Additionally,the practical application of regional cultural elements is examined,in order to offer guidance for the application of cultural creation of traditional characteristic villages in rural public spaces.展开更多
In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main re...In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main results generalize and extend several well-known comparable results from the existing literature.Moreover,some examples are provided to illustrate the main results.展开更多
Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Le...Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Lebesgue space which has vanishing moments up to order s plays an important role,where s∈N.展开更多
In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total vari...In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.展开更多
The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu...The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.展开更多
In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequen...In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey...In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).展开更多
The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces....The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.展开更多
Integrating autonomous vehicles (AVs) and autonomous parking spaces (APS) marks a transformative development in urban mobility and sustainability. This paper reflects on these technologies’ historical evolution, curr...Integrating autonomous vehicles (AVs) and autonomous parking spaces (APS) marks a transformative development in urban mobility and sustainability. This paper reflects on these technologies’ historical evolution, current interdependence, and future potential through the lens of environmental, social, and economic sustainability. Historically, parking systems evolved from manual designs to automated processes yet remained focused on convenience rather than sustainability. Presently, advancements in smart infrastructure and vehicle-to-infrastructure (V2I) communication have enabled AVs and APS to operate as a cohesive system, optimizing space, energy, and transportation efficiency. Looking ahead, the seamless integration of AVs and APS into broader smart city ecosystems promises to redefine urban landscapes by repurposing traditional parking infrastructure into multifunctional spaces and supporting renewable energy initiatives. These technologies align with global sustainability goals by mitigating emissions, reducing urban sprawl, and fostering adaptive land uses. This reflection highlights the need for collaborative efforts among stakeholders to address regulatory and technological challenges, ensuring the equitable and efficient deployment of AVs and APS for smarter, greener cities.展开更多
U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admittin...U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admitting reflections by using U_(S)-admitting determined sets.展开更多
We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function ...We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm;in particular,we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.展开更多
In this paper we investigate the existence of solution for the following nonlocal problem with Stein-Weiss convolution term-△Φu+V(x)Φ(|u|)u=1/|x|α(∫R^(N)K(y)F(u(y))/|x-y|Y(λ)|y|^(α)dy)K(x)f(u(x)),x∈R^(N),where...In this paper we investigate the existence of solution for the following nonlocal problem with Stein-Weiss convolution term-△Φu+V(x)Φ(|u|)u=1/|x|α(∫R^(N)K(y)F(u(y))/|x-y|Y(λ)|y|^(α)dy)K(x)f(u(x)),x∈R^(N),where α≥0,N≥2,λ>0 is a positive parameter,V,K∈C(R^(N),[0,∞))are nonne-gative functions that may vanish at infinity,the function f ∈ C(R,R)is quasicritical and F(t)=∫_(0)^(t)f(s)ds.To establish our existence and regularity results,we use the Hardy-type inequalities for Orlicz-Sobolev Space and the Stein-Weiss inequality together with a varia-tional technique based on the mountain pass theorem for a functional that is not necessarily in C'.Furthermore,we also prove the existence of a ground state solution by the method of Nehari manifold in the case where the strict monotonicity condition on f is not required.This work incorporates the case where the N-function Φdoes not verify the △_(2)-condition.展开更多
This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author...This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.展开更多
基金Supported by the National Natural Science Foundation of China(11871195)。
文摘In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.
基金Thanks to the Education Department of the Basque Government for conceding a grant to Aimar Santos-Garcia(Grant No.PRE_2023_2_0237),giving financial support for developing a PhD thesis,and to the Department of Architecture of the University of the Basque Country for funding the publication of this paper.
文摘Experts question why cities, which are supposedly built for citizens, fail to addresstheir social needs. Everyday life is challenging in our cities, especially because public spaceshave generally been arranged and designed by considering the physical environment and withoutconsideration for how these spaces should facilitate human interactions. This paper identifies“in-between spaces” as key scenarios for addressing this issue. These spaces offer the opportunity to feel comfortable and safe, foster a sense of community, and facilitate connections.Little has been written about these spaces and, particularly, their characteristics. Therefore,the objective of this study is to provide a more in-depth understanding of in-between spaces byexamining literature on such spaces throughout city history.The results underscore the threshold character as the primary feature of in-between spacesand define various types of in-between spaces depending on their position within the gradientbetween public and private domains. The analysis also identified recurring characteristics, suchas presence of reproductive labor, vegetation, or amenities, tendency to be programmed or unprogrammed within interior or exterior spaces and establishes relationships between these characteristics. Furthermore, the results suggest that the values promoted by these spaces and theirrecurring features can offer solutions to regenerate cities.
基金We would like to express our gratitude to the Autonomous University of Baja California(UABC),the Master's and Doctoral Program in Architecture,Urbanism and Design(MyDAUD),as well as the National Council of Science and Technology(Conacyt).The project is linked to the paper:Habitability and post-covid.A study of urban connectivity in public,which has as code:402/3412.This project is internal to the university and it does not have funds.
文摘This study reflects on the impact that the neighborhoods’in-between spaces have on:spatial perception,social interaction,and security.These sites,characterized by their abandonment and deterioration,can also be seen as crucial spaces of opportunity for cities,in the architectural,urban and landscape research.This paper aims to analyze the sociospatial relationships in the neighborhoods’in-between spaces and examine the impact of inbetween space configuration on urban habitability.The investigation draws on a survey of perception to residents about the requirements for a suitable social interaction in these spaces.This study was developed in a neighborhood in the city periphery,characterized by their social dynamics and location in a nature conservation area.The findings indicate that the appropriation process,activities,and collective practices are dependent on the spatial legibility,in this case when this increases,gives rise to improve the habitability and the rehabilitation of the in-between space.Furthermore,the lack of design on in-between spaces substantially affects the use of these spaces and the social interaction among residents.
基金The authors are grateful to Prof.Mazouz Said and Dr.Can Isin for their valuable advice during this research.They alsq thank Zerouati Maouahib and Bensaadi Karim for their invaluable help in conducting snapshot observation.
文摘This research examines the impact of in-between space configuration on users'social practices.The effects of different degrees of permeability of these spaces on the social interactions of the inhabitants are also analyzed.This research is based on a comparative approach using space syntax analysis and snapshot observations on four mass housing neighborhoods in Serif,Algeria.The neighborhoods are selected according to their degree of permeability,location in the city,realization period,and syntax measures from integrated to segregated.The activity patterns of two-week days for each study case are observed and recorded.Correlation results of observed social activities and syntactic measures demonstrate that spatial configuration affects people's use of in-between spaces.Moreover,connectivity and clustering coefficients are revealed to be important indicators of social activities.Previous urban studies argued that integrated spaces are mostly used by people.However,social interaction in the studied cases increases in the least connected areas,adjoining spaces to the buildings,and most closed spaces.This research finds that social activities are dependent on the degree of permeability,which when low,gives rise to increased social interaction and activities.
基金supported by the China Scholarship Council(Grant No.202306690024)the Ministerio de Ciencia e Innovación and Fondos FEDER(Grant Nos.PID2021-562126509OB-C21 and PDC2022-133332-C21)+1 种基金the Generalitat de Catalunya(Grant No.2021SGR00138)the Beatriu de Pinós Fellowship(Grant No.2021-BP-00206).
文摘Depolarizing behavior is commonly observed in most natural samples.For this reason,optical tools measuring the differences in depolarization response among spatially separated structures are highly useful in a wide range of imaging applications for enhanced visualization of structures,target identification,etc.One commonly used tool for depolarizing discrimination is the so-called depolarizing spaces.In this article,we exploit the combined use of two depolarizing spaces,the indices of polarization purity(IPP)and polarizance–reflection–transformation(PRT)spaces,to improve the capability of optical systems to identify polarization–anisotropy depolarizers.The potential of these spaces to discriminate among different depolarizers is first studied from a series of simulations by incoherently adding diattenuations or retarders,with some control parameters emulating samples in nature.The simulated results demonstrate that the proposed methods are capable of increasing differences among depolarizers beyond other well-known techniques.Experimentally,validation is provided by conducting diverse phantom experiments of easy interpretation and mimicking the stated simulations.As a useful application of our approach,we developed a model able to retrieve intrinsic microscopic information of samples from macroscopic polarimetric measurements.The proposed methods enable non-invasive,straightforward,macroscopic characterization of depolarizing samples,and may be of interest for enhanced visualization of samples in multiple imaging scenarios.
文摘In the context of rural revitalization,the landscape design of public spaces in Enshi Xiaomaopoying Village presents both new opportunities and challenges.This study explores the significance of integrating regional culture into rural public spaces.Field research has been conducted to assess the current utilization of regional culture in the public spaces of Xiaomaopoying Village.Subsequently,design optimization strategies are analyzed and proposed.Additionally,the practical application of regional cultural elements is examined,in order to offer guidance for the application of cultural creation of traditional characteristic villages in rural public spaces.
基金Supported by the National Natural Science Foundation of China(12001249)the Natural Science Foundation of Jiangxi Province(20232BAB211004)the Educational Commission Science Programm of Jiangxi Province(GJJ2200523)。
文摘In this paper,we establish common fixed point theorems for expansive map?pings on b-metric-like space and coincidence point for f-weakly isotone increasing mappings in partially ordered b-metric-like space.The main results generalize and extend several well-known comparable results from the existing literature.Moreover,some examples are provided to illustrate the main results.
文摘Inhomogeneous Calderon-Zygmund operator T maps each atom into an approximate molecule of weighted local Hardy space if and only if some approximate cancellation condition holds for T.An equivalent norm for weighted Lebesgue space which has vanishing moments up to order s plays an important role,where s∈N.
基金Supported in part by NSFC(No.11971005)the Fundamental Research Funds for the Central Universities(Nos.GK202101008,GK202102012)。
文摘In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.
基金Supported by the National Natural Science Foundation of China(12301101)the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
文摘In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
文摘In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).
基金Supported by NSFC(No.12171062)the Natural Science Foundation of Chongqing(No.CSTB2022NSCQ-JQX0004)+1 种基金the Chongqing Talent Support Program(No.cstc2024ycjh-bgzxm0121)Science and Technology Project of Chongqing Education Committee(No.KJZD-M202300503)。
文摘The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.
文摘Integrating autonomous vehicles (AVs) and autonomous parking spaces (APS) marks a transformative development in urban mobility and sustainability. This paper reflects on these technologies’ historical evolution, current interdependence, and future potential through the lens of environmental, social, and economic sustainability. Historically, parking systems evolved from manual designs to automated processes yet remained focused on convenience rather than sustainability. Presently, advancements in smart infrastructure and vehicle-to-infrastructure (V2I) communication have enabled AVs and APS to operate as a cohesive system, optimizing space, energy, and transportation efficiency. Looking ahead, the seamless integration of AVs and APS into broader smart city ecosystems promises to redefine urban landscapes by repurposing traditional parking infrastructure into multifunctional spaces and supporting renewable energy initiatives. These technologies align with global sustainability goals by mitigating emissions, reducing urban sprawl, and fostering adaptive land uses. This reflection highlights the need for collaborative efforts among stakeholders to address regulatory and technological challenges, ensuring the equitable and efficient deployment of AVs and APS for smarter, greener cities.
基金Supported by the National Natural Science Foundation of China(Grant No.12571507)。
文摘U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admitting reflections by using U_(S)-admitting determined sets.
文摘We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm;in particular,we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.
基金supported by FAPESQ/Brazil(Grant No.3031/2021)supported by CNPq/Brazil(Grant No.309.692/2020-2)
文摘In this paper we investigate the existence of solution for the following nonlocal problem with Stein-Weiss convolution term-△Φu+V(x)Φ(|u|)u=1/|x|α(∫R^(N)K(y)F(u(y))/|x-y|Y(λ)|y|^(α)dy)K(x)f(u(x)),x∈R^(N),where α≥0,N≥2,λ>0 is a positive parameter,V,K∈C(R^(N),[0,∞))are nonne-gative functions that may vanish at infinity,the function f ∈ C(R,R)is quasicritical and F(t)=∫_(0)^(t)f(s)ds.To establish our existence and regularity results,we use the Hardy-type inequalities for Orlicz-Sobolev Space and the Stein-Weiss inequality together with a varia-tional technique based on the mountain pass theorem for a functional that is not necessarily in C'.Furthermore,we also prove the existence of a ground state solution by the method of Nehari manifold in the case where the strict monotonicity condition on f is not required.This work incorporates the case where the N-function Φdoes not verify the △_(2)-condition.
基金Supported by the Key Project of the Education Department of Fujian Province(JZ230054)the Sanming University's High-Level Talent Introduction Project(23YG09)the Natural Science Foundation of Fujian Province(2024J01903)。
文摘This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.
