Boundedness of Singular Integral Operators on Herz-Morrey Spaces with Variable Exponent

Citation:

Hongbin WANG,Fanghui LIAO.Boundedness of Singular Integral Operators on Herz-Morrey Spaces with Variable Exponent[J].Chinese Annals of Mathematics B,2020,41(1):99~116
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Authors:

Hongbin WANG; Fanghui LIAO

Foundation:

This work was supported by the National Natural Science Foundation of China (No.11761026), Shandong Provincial Natural Science Foundation of China (No.ZR2017MA041) and the Project of Shandong Province Higher Educational Science and Technology Program (No.J18KA225).
Abstract: Let $\Omega\in L^s(\mathrm{S}^{n-1}) \ (s>1)$ be a homogeneous function of degree zero and $b$ be a BMO function or Lipschitz function. In this paper, the authors obtain some boundedness of the Calder\'{o}n-Zygmund singular integral operator $T_\Omega$ and its commutator $[b,T_\Omega]$ on Herz-Morrey spaces with variable exponent.

Keywords:

Calder'{o}n-Zygmund singular integral, Commutator, Herz-Morrey space, Variable exponent

Classification:

42B20, 42B35, 46E30
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