TY - JOUR T1 - Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces JO - Analysis in Theory and Applications VL - 1 SP - 90 EP - 102 PY - 2016 DA - 2016/01 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n1.8 UR - https://global-sci.org/intro/article_detail/ata/4657.html KW - Toeplitz type operator, singular integral operator, variable Calder¤în-Zygmund kernel, weighted BMO function, weighted Lipschitz function, weighted Morrey space. AB -

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.