In this paper,the authors introduce certain Herz type Hardy spaces with variable exponents and establish the characterizations of these spaces in terms of atomic and molecular decompositions. Using these decomposition...In this paper,the authors introduce certain Herz type Hardy spaces with variable exponents and establish the characterizations of these spaces in terms of atomic and molecular decompositions. Using these decompositions,the authors obtain the boundedness of some singular integral operators on the Herz type Hardy spaces with variable exponents.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.
In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this a...In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-H¨older continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces.展开更多
The boundedness of multilinear Calderdn-Zygmund operators and their commutators with bounded mean oscillation (BMO) functions in variable exponent Morrey spaces are obtained.
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 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
We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decompositio...We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.展开更多
基金partially supported by the NSF of China (Grants No.11361020)the Natural Science Foundation of Hainan Province (No.20151011)
文摘In this paper,the authors introduce certain Herz type Hardy spaces with variable exponents and establish the characterizations of these spaces in terms of atomic and molecular decompositions. Using these decompositions,the authors obtain the boundedness of some singular integral operators on the Herz type Hardy spaces with variable exponents.
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 by the Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology(Grant No.2017r098)Zunwei Fu was supported by National Natural Science Foundation of China(Grant Nos.11671185 and 11771195)+1 种基金National Science Foundation of Shandong Province(Grant No.ZR2017MA041)Jingshi Xu was supported by National Natural Science Foundation of China(Grant No.11761026)
文摘In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-H¨older continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces.
基金The first author was supported by the TianYuan Special Funds of the National Natural Science Foundation of China (Grant No. 11426221) and the High Level Introduction of Talent Research Start-up Fund by Central South University of Forestory and Technology (Grant No. 1040212) the second author was supported by the National Natural Science Foundation of China (Grant No. 11361020).
文摘The boundedness of multilinear Calderdn-Zygmund operators and their commutators with bounded mean oscillation (BMO) functions in variable exponent Morrey spaces are obtained.
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 in part by the National Natural Science Foundation of China(Grant No.11761026,11761027)Natural Science Foundation of Guangxi(Grant No.2020GXNSFAA159085).
文摘We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.