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Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent 被引量:6
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作者 Lijuan Wang Shuangping Tao 《Analysis in Theory and Applications》 CSCD 2015年第1期13-24,共12页
In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley... In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^*- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained. 展开更多
关键词 Parameterized Littlewood-Paley operators COMMUTATORS lebesgue spaces with variable exponent.
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Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition
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作者 Mohamed Karimou Gazibo Duni Yegbonoma Frédéric Zongo 《Applied Mathematics》 2024年第7期455-463,共9页
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
关键词 lebesgue and Sobolev spaces with variable exponent Weak Solution Entropy Solution Degenerate Parabolic-Hyperbolic Equation Conservation Law Leray Lions Type Operator Neumann Boundary Condition Existence Result
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Riesz-Kolmogorov theorem in variable exponent Lebesgue spaces and its applications to Riemann-Liouville fractional differential equations 被引量:2
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作者 Baohua Dong Zunwei Fu Jingshi Xu 《Science China Mathematics》 SCIE CSCD 2018年第10期1807-1824,共18页
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
关键词 lebesgue space with variable exponent Riesz-Kolmogorov theorem Riemann-Liouville fractionalcalculus fixed-point theorem
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