We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-orde...We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-order convection term.By employing innovative integralbased test functions,we derive the necessary a priori estimates.To prove the convergence of solutions to the degenerate coercivity problem,we adopt a method that combines monotonicity and truncation techniques.This approach allows us to demonstrate that the gradient sequences converge almost everywhere.展开更多
We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.展开更多
In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） an...In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.展开更多
In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mappi...In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicated estimate.展开更多
Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are v...Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents.Furthermore, we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.展开更多
The purpose of this paper is to study a class of elliptic equations with variable exponents. By using the method of regularization and a priori estimates, we obtain the existence of weak solutions to these problems.
In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [b,μ<sub>Ω</sub>] and obtain the result with Lipschitz function and BMO function f on t...In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [b,μ<sub>Ω</sub>] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents <img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" width="0" height="0" alt="" /><img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" alt="" />.展开更多
We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions,dispersion,source,and variable-exponents.We discovered that the solution of the system is global and con...We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions,dispersion,source,and variable-exponents.We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions.After that,it is demonstrated that the blow-up has negative initial energy.Subsequently,the growth of solutions is demonstrated with positive initial energy,and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.展开更多
In this paper, we introduce Morrey-Herz spaces MKq.p（·）α（·）,λ with variable exponents α（·） and p（·）, and prove the boundedness of multilinear Calderdn-Zygmund singular operators on the ...In this paper, we introduce Morrey-Herz spaces MKq.p（·）α（·）,λ with variable exponents α（·） and p（·）, and prove the boundedness of multilinear Calderdn-Zygmund singular operators on the product of these spaces.展开更多
The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity,and L^(1)-data.The functional setting involves Lebesgue-Sobolev spaces with variable exponents.W...The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity,and L^(1)-data.The functional setting involves Lebesgue-Sobolev spaces with variable exponents.We prove the existence of an entropy solution and show its continuous dependence on the L^(1)-data in W^(1.q(-))(Ω)with some q(.)>1.展开更多
This paper is devoted to the study of a nonlinear anisotropic elliptic e-quation with degenerate coercivity,lower order term and L1 datum in appropriate anisotropic variable exponents Sobolev spaced We obtain the exis...This paper is devoted to the study of a nonlinear anisotropic elliptic e-quation with degenerate coercivity,lower order term and L1 datum in appropriate anisotropic variable exponents Sobolev spaced We obtain the existence of distributional solutions.展开更多
In this paper,the authors obtain the boundedness of vector valued bilinear Calderón-Zygmund operators on products of weighted Herz-Morrey spaces with variable exponents.
We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents.Based on this result,we obtain the boundedness for the multilinear si...We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents.Based on this result,we obtain the boundedness for the multilinear singular integral operators and two kinds of multilinear singular integral commutators on the above spaces.展开更多
In this paper,we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of two weighted Herz spaces.
We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its co...We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its commutator.展开更多
In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions.Then we obtain decomposition characterizations of these spaces by atom,molecule and wavele...In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions.Then we obtain decomposition characterizations of these spaces by atom,molecule and wavelet.As an application,we obtain the boundedness of the pseudo-differential operators on these spaces.展开更多
After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some ...After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.展开更多
We prove some boundedness results for a large class of sublinear operators with rough kernel on the homogeneous Herz spaces where the three main indices are variable exponents.Some known results are extended.
In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator esti...In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.展开更多
We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition a...We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11901131)。
文摘We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-order convection term.By employing innovative integralbased test functions,we derive the necessary a priori estimates.To prove the convergence of solutions to the degenerate coercivity problem,we adopt a method that combines monotonicity and truncation techniques.This approach allows us to demonstrate that the gradient sequences converge almost everywhere.
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
基金supported by NSFC (No. 11201003)Education Committee of Anhui Province (No. KJ2012A133)
文摘In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.
文摘In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicated estimate.
文摘Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents.Furthermore, we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.
文摘The purpose of this paper is to study a class of elliptic equations with variable exponents. By using the method of regularization and a priori estimates, we obtain the existence of weak solutions to these problems.
文摘In this paper, our aim is to prove the boundedness of commutators generated by the Marcinkiewicz integrals operator [b,μ<sub>Ω</sub>] and obtain the result with Lipschitz function and BMO function f on the Herz-Morrey-Hardy spaces with variable exponents <img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" width="0" height="0" alt="" /><img src="Edit_04b1c6c8-570f-4eb1-bb9c-047352a8c1cc.bmp" alt="" />.
文摘We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions,dispersion,source,and variable-exponents.We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions.After that,it is demonstrated that the blow-up has negative initial energy.Subsequently,the growth of solutions is demonstrated with positive initial energy,and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271209 and 11371370)NaturalScience Foundation of Nantong University(Grant No.11ZY002)
文摘In this paper, we introduce Morrey-Herz spaces MKq.p（·）α（·）,λ with variable exponents α（·） and p（·）, and prove the boundedness of multilinear Calderdn-Zygmund singular operators on the product of these spaces.
文摘The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity,and L^(1)-data.The functional setting involves Lebesgue-Sobolev spaces with variable exponents.We prove the existence of an entropy solution and show its continuous dependence on the L^(1)-data in W^(1.q(-))(Ω)with some q(.)>1.
文摘This paper is devoted to the study of a nonlinear anisotropic elliptic e-quation with degenerate coercivity,lower order term and L1 datum in appropriate anisotropic variable exponents Sobolev spaced We obtain the existence of distributional solutions.
基金supported by the National Natural Science Foundation of China(Nos.11761026)Guangxi Natural Science Foundation(No.2020GXNSFAA159085)。
文摘In this paper,the authors obtain the boundedness of vector valued bilinear Calderón-Zygmund operators on products of weighted Herz-Morrey spaces with variable exponents.
基金supported in part by the National Natural Science Foundationof China(Grant Nos.11926343,11926342,11761026)the Natural Science Foundation of Guangxi Province(Grant No.2020GXNSFAA159085)the Open Project of Anhui University(Grant No.KF2019B02).
文摘We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents.Based on this result,we obtain the boundedness for the multilinear singular integral operators and two kinds of multilinear singular integral commutators on the above spaces.
基金supported by the National Natural Science Foundation of China(Grant No.11761026)Guangxi Natural Science Foundation(Grant No.2020GXNSFAA159085).
文摘In this paper,we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of two weighted Herz spaces.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11671397,12071473).
文摘We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its commutator.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12161022 and 12061030)Hainan Provincial Natural Science Foundation of China(Grant No.122RC652)the Science and Technology Project of Guangxi(Grant No.Guike AD23023002)。
文摘In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions.Then we obtain decomposition characterizations of these spaces by atom,molecule and wavelet.As an application,we obtain the boundedness of the pseudo-differential operators on these spaces.
文摘After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.
基金Natural Science Foundation of Education Committee of Anhui Province(No.KJ2019A1196)Anhui Provincial Natural Science Foundation(No.1908085MA19)Preresearch Project of the NNSF of China(No.2019yyzrl4).
文摘We prove some boundedness results for a large class of sublinear operators with rough kernel on the homogeneous Herz spaces where the three main indices are variable exponents.Some known results are extended.
文摘In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.
文摘We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.
