Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Year:    2016

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 90–102

Abstract

Suppose $T^{k,1}$ and $T^{k,2}$ are singular integrals with variable kernels and mixed homogeneity or $\pm I$ (the identity operator). Denote the Toeplitz type operator by\begin{align*}T^b=\sum_{k=1}^QT^{k,1}M^bT^{k,2}, \end{align*} where $M^bf=bf.$ In this paper, the boundedness of $T^b$ on weighted Morrey space are obtained when $b$ belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2016.v32.n1.8

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 90–102

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Toeplitz type operator singular integral operator variable Calderόn-Zygmund kernel weighted BMO function weighted Lipschitz function weighted Morrey space.