Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces
Pure and Applied Mathematics Journal
Volume 8, Issue 1, February 2019, Pages: 18-29
Received: Mar. 23, 2019; Accepted: Apr. 22, 2019; Published: May 9, 2019
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Junmei Wang, School of Mathematics and Statistics, Shandong Normal University, Jinan, China; School of Mathematics and Statistics, Linyi University, Linyi, China
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In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.
Weighted Grand Morrey Space, Sublinear Operator, Rough Kernel, Commutator
To cite this article
Junmei Wang, Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces, Pure and Applied Mathematics Journal. Vol. 8, No. 1, 2019, pp. 18-29. doi: 10.11648/j.pamj.20190801.13
Copyright © 2019 Authors retain the copyright of this article.
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