The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′...The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.展开更多
Local Climate Zones(LCZs)provide a standardized framework for analyzing urban thermal environment.Examining the interactive effects of building and green space patterns on land surface temperature(LST)within LCZs is e...Local Climate Zones(LCZs)provide a standardized framework for analyzing urban thermal environment.Examining the interactive effects of building and green space patterns on land surface temperature(LST)within LCZs is essential for uncovering urban cooling mechanisms and developing strategies for heat-mitigation urban design.Therefore,this study employed one-way ANOVA and Duncan's multiple comparison to test compare the significant differences of LST among LCZs 1-6,and applied the XGBoost model to quantify the interactive effects of building and green space indicators on LST,and to identify the threshold ranges of their cooling effects.The results showed that LCZ 2 exhibited the highest LST,while LCZ 4 recorded the lowest.Average building volume(BAV),building coverage ratio(BCR),green cover area(GCA),and the total edge length of green space(GTE)were identified as the key indicators driving the interactive effects on LST.In LCZ 2,when BAV exceeded 1800 m^(3),the interaction of higher GCA and GTE contributed to lower LST.When BCR was less than 0.6 in LCZs 4-5,lower GCA and GTE values enhanced the LST reduction.The results provided a strategic basis for urban thermal environment mitigation and sustainable development under the LCZ framework.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 into ℂ.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 into ℂ.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 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
In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for t...In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.展开更多
The Gansu-Qinghai contiguous region of the upper Yellow River is located in the transition zone between the Loess Plateau and the Qinghai-Tibet Plateau,characterized by fragile ecosystems and high sensitivity to clima...The Gansu-Qinghai contiguous region of the upper Yellow River is located in the transition zone between the Loess Plateau and the Qinghai-Tibet Plateau,characterized by fragile ecosystems and high sensitivity to climate change.As a critical ecological security barrier and water conservation area,it faces persistent tensions between development demands and ecological protection.Quantitative assessments of how production-living-ecological space(PLES)evolution affects ecological and environmental quality(EEQ)under long-term,multi-scenario conditions remain limited in such vulnerable regions.Understanding PLES-EEQ relationships is essential for optimizing territorial spatial planning and maintaining ecological security in the Yellow River basin.This study utilized land use data from 2000 to 2020 and the FLUS model to simulate PLES evolution from 2030 to 2060 under SSP1,SSP2,and SSP5 scenarios.The analytical framework integrated artificial neural networks and cellular automata with Shared Socioeconomic Pathways to project spatial configurations and assess EEQ in 2035.Living space expanded across all three scenarios while ecological space decreased.Production space increased by 125 km^(2) under SSP5 but declined in other scenarios.The EEQ index in 2035 showed improvements relative to the baseline value(0.4130)in 2020.Medium-to-high quality areas were primarily grassland and forest,whereas low-quality areas consisted mainly of unused land concentrated in the central and western regions.This study reveals a nonlinear relationship between ecological space quantity and quality,showing that structural optimization can enhance EEQ despite area reduction.The findings suggest that strengthening ecological protection redlines and restraining urban expansion are essential for territorial spatial optimization in ecologically fragile regions.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:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) contain...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:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) 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 article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
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
In this paper,we first obtain the density of compactly supported bounded functions in anisotropic infinite dimensional Banach space-valued Musielak-Orlicz spaces.Then,we present the sufficient condition for the space ...In this paper,we first obtain the density of compactly supported bounded functions in anisotropic infinite dimensional Banach space-valued Musielak-Orlicz spaces.Then,we present the sufficient condition for the space of compactly supported smooth functions to be dense in anisotropic infinite dimensional Banach space-valued Musielak-Orlicz spaces.Moreover,the modular density is also given.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
This paper is a continuation of[Erguang YANG.On some generalized countably compact spaces.J.Math.Res.Appl.,2019,39(5):540–550]in which characterizations of some generalized countably compact spaces such as quasi-γsp...This paper is a continuation of[Erguang YANG.On some generalized countably compact spaces.J.Math.Res.Appl.,2019,39(5):540–550]in which characterizations of some generalized countably compact spaces such as quasi-γspaces,quasi-Nagata spaces,wN-spaces and wM-spaces in terms of real-valued functions were obtained.In this paper,we shall present some other forms of characterizations of the spaces mentioned above.展开更多
The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and ...The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.展开更多
We first give alternative expressions of some generalized countably compact spaces such as quasi-γspaces, quasi-Nagata spaces, M^#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present...We first give alternative expressions of some generalized countably compact spaces such as quasi-γspaces, quasi-Nagata spaces, M^#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present some characterizations of the corresponding spaces with real-valued functions.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
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
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
In modal logic,topological semantics is an intuitive and natural special case of neighbourhood semantics.This paper stems from the observation that the satisfaction relation of topological semantics applies to subset ...In modal logic,topological semantics is an intuitive and natural special case of neighbourhood semantics.This paper stems from the observation that the satisfaction relation of topological semantics applies to subset spaces which are more general than topological spaces.The minimal modal logic which is strongly sound and complete with respect to the class of subset spaces is found.Soundness and completeness results of some famous modal logics(e.g.S4,S5 and Tr)with respect to various important classes of subset spaces(eg intersection structures and complete fields of sets)are also proved.In the meantime,some known results,e.g.the soundness and completeness of Tr with respect to the class of discrete topological spaces,are proved directly using some modifications of the method of canonical mode1,without a detour via neighbourhood semantics or relational semantics.展开更多
基金Supported by Natural Science Foundation of China(12461021)。
文摘The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.
基金financial support from the National Natural Science Foundation of China(32271661,32130068).
文摘Local Climate Zones(LCZs)provide a standardized framework for analyzing urban thermal environment.Examining the interactive effects of building and green space patterns on land surface temperature(LST)within LCZs is essential for uncovering urban cooling mechanisms and developing strategies for heat-mitigation urban design.Therefore,this study employed one-way ANOVA and Duncan's multiple comparison to test compare the significant differences of LST among LCZs 1-6,and applied the XGBoost model to quantify the interactive effects of building and green space indicators on LST,and to identify the threshold ranges of their cooling effects.The results showed that LCZ 2 exhibited the highest LST,while LCZ 4 recorded the lowest.Average building volume(BAV),building coverage ratio(BCR),green cover area(GCA),and the total edge length of green space(GTE)were identified as the key indicators driving the interactive effects on LST.In LCZ 2,when BAV exceeded 1800 m^(3),the interaction of higher GCA and GTE contributed to lower LST.When BCR was less than 0.6 in LCZs 4-5,lower GCA and GTE values enhanced the LST reduction.The results provided a strategic basis for urban thermal environment mitigation and sustainable development under the LCZ framework.
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 into ℂ.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 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 Science and Technology Development Plan Project of Jilin Province China(Grant No.20260102245JC)Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.
基金funded by the National Natural Science Foundation of China(Grant No.42461038 and No.42161043).
文摘The Gansu-Qinghai contiguous region of the upper Yellow River is located in the transition zone between the Loess Plateau and the Qinghai-Tibet Plateau,characterized by fragile ecosystems and high sensitivity to climate change.As a critical ecological security barrier and water conservation area,it faces persistent tensions between development demands and ecological protection.Quantitative assessments of how production-living-ecological space(PLES)evolution affects ecological and environmental quality(EEQ)under long-term,multi-scenario conditions remain limited in such vulnerable regions.Understanding PLES-EEQ relationships is essential for optimizing territorial spatial planning and maintaining ecological security in the Yellow River basin.This study utilized land use data from 2000 to 2020 and the FLUS model to simulate PLES evolution from 2030 to 2060 under SSP1,SSP2,and SSP5 scenarios.The analytical framework integrated artificial neural networks and cellular automata with Shared Socioeconomic Pathways to project spatial configurations and assess EEQ in 2035.Living space expanded across all three scenarios while ecological space decreased.Production space increased by 125 km^(2) under SSP5 but declined in other scenarios.The EEQ index in 2035 showed improvements relative to the baseline value(0.4130)in 2020.Medium-to-high quality areas were primarily grassland and forest,whereas low-quality areas consisted mainly of unused land concentrated in the central and western regions.This study reveals a nonlinear relationship between ecological space quantity and quality,showing that structural optimization can enhance EEQ despite area reduction.The findings suggest that strengthening ecological protection redlines and restraining urban expansion are essential for territorial spatial optimization in ecologically fragile regions.
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:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) 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 Chizhou University High Level Talent Research Start up Fund (No.CZ2025YJRC52)。
文摘In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
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 National Natural Science Foundation of China(Grant No.12161022)the Science and Technology Project of Guangxi(Grant No.Guike AD23023002).
文摘In this paper,we first obtain the density of compactly supported bounded functions in anisotropic infinite dimensional Banach space-valued Musielak-Orlicz spaces.Then,we present the sufficient condition for the space of compactly supported smooth functions to be dense in anisotropic infinite dimensional Banach space-valued Musielak-Orlicz spaces.Moreover,the modular density is also given.
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<∞).
文摘This paper is a continuation of[Erguang YANG.On some generalized countably compact spaces.J.Math.Res.Appl.,2019,39(5):540–550]in which characterizations of some generalized countably compact spaces such as quasi-γspaces,quasi-Nagata spaces,wN-spaces and wM-spaces in terms of real-valued functions were obtained.In this paper,we shall present some other forms of characterizations of the spaces mentioned above.
文摘The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.
基金Supported by the National Natural Science Foundation of China(Grant No.11401262)
文摘We first give alternative expressions of some generalized countably compact spaces such as quasi-γspaces, quasi-Nagata spaces, M^#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present some characterizations of the corresponding spaces with real-valued functions.
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.
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.
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
基金supported by the National Social Science Fund of China(No.20CZX048)。
文摘In modal logic,topological semantics is an intuitive and natural special case of neighbourhood semantics.This paper stems from the observation that the satisfaction relation of topological semantics applies to subset spaces which are more general than topological spaces.The minimal modal logic which is strongly sound and complete with respect to the class of subset spaces is found.Soundness and completeness results of some famous modal logics(e.g.S4,S5 and Tr)with respect to various important classes of subset spaces(eg intersection structures and complete fields of sets)are also proved.In the meantime,some known results,e.g.the soundness and completeness of Tr with respect to the class of discrete topological spaces,are proved directly using some modifications of the method of canonical mode1,without a detour via neighbourhood semantics or relational semantics.
