Abstract
In this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.
Funding source: Hakkari University Scientific Research Project
Award Identifier / Grant number: FM18BAP1
Funding source: Institution of Higher Education Scientific Research Project in Ningxia
Award Identifier / Grant number: NGY2017011
Funding source: Natural Science Foundation of China
Award Identifier / Grant number: 11461053
Award Identifier / Grant number: 11762016
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work is funded by Hakkari University Scientific Research Project (Grant no. FM18BAP1) under the research project “Some estimates for rough Riesz type potential operator with variable order and rough fractional maximal operator with variable order both on generalized variable exponent Morrey spaces and vanishing generalized variable exponent Morrey spaces”, Institution of Higher Education Scientific Research Project in Ningxia (Grant no. NGY2017011) and Natural Science Foundation of China (Grant nos. 11461053 and 11762016).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Research on prediction model of thermal and moisture comfort of underwear based on principal component analysis and Genetic Algorithm–Back Propagation neural network
- Design of the state feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type overhead cranes with time-varying hoisting rope length
- Blowup and global existence of mild solutions for fractional extended Fisher–Kolmogorov equations
- Lipschitz stability of nonlinear ordinary differential equations with non-instantaneous impulses in ordered Banach spaces
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- New technique for the approximation of the zeros of nonlinear scientific models
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