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
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X intoℂ.As applications,we will establish refined Bohr ...In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X intoℂ.As applications,we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball BX with values in higher dimensional spaces.Next,we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on BX.In addition,we establish an improved version of the Bohr inequality for holomorphic functions on BX.All the results are proved to be sharp.展开更多
In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[...In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).展开更多
Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:■contains■-uniformly copies of■.in the case p^(*)>n(ii)■containsλ^(n)-uniformly cop...Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:■contains■-uniformly copies of■.in the case p^(*)>n(ii)■containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.展开更多
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer...In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.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
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supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
基金supported by the SERB,SUR/2022/002244,Govt.India and the second author was supported by the UGC-JRF(NTA Ref.No.:201610135853)New Delhi,India,and the third author was partially supported by the JSPS KAKENHI(JP22K03363).
文摘In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X intoℂ.As applications,we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball BX with values in higher dimensional spaces.Next,we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on BX.In addition,we establish an improved version of the Bohr inequality for holomorphic functions on BX.All the results are proved to be sharp.
基金supported by the Fundamental Research Program of Shanxi Province(202103021223038).
文摘In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).
文摘Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:■contains■-uniformly copies of■.in the case p^(*)>n(ii)■containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.
基金supported by the National Natural Science Foundation of China(11601525)the Natural Science Foundation of Hunan Province(2024JJ5412),the Changsha Municipal Natural Science Foundation(kq2402193).
文摘In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.
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.
