Volume 35, Issue 4
Weighted Norm Inequalities for Toeplitz Type Operator Related to Singular Integral Operator with Variable Kernel

Yuexiang He

10.4208/ata.OA-2018-1012

Anal. Theory Appl., 35 (2019), pp. 377-391.

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  • Abstract

Let $T^{k,1}$  be the singular integrals with variable Calder\'on-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.


  • History

Published online: 2020-01

  • AMS Subject Headings

42B20, 42B25

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