Weighted Norm Inequalities for Toeplitz Type Operator Related to Singular Integral Operator with Variable Kernel
Year: 2019
Author: Yuexiang He
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 4 : pp. 377–391
Abstract
Let $T^{k,1}$ be the singular integrals with variable Calderόn-Zygmund kernels or $\pm I$ (the identity operator), let $T^{k,2}$ and $T^{k,4}$ be the linear operators, and let $T^{k,3}=\pm I$. Denote the Toeplitz type operator by
$$T^b=\sum_{k=1}^t(T^{k,1}M^bI_\alpha T^{k,2}+T^{k,3}I_\alpha M^b T^{k,4}),$$
where $M^bf=bf,$ and $I_\alpha$ is the fractional integral operator. In this paper, we investigate the boundedness of the operator on weighted Lebesgue space when $b$ belongs to weighted Lipschitz space.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2018-1012
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 4 : pp. 377–391
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Toeplitz type operator variable Calderόn-Zygmund kernel fractional integral weighted Lipschitz space.