Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space

Abstract

Let $T_{1}$ be a singular integral with non-smooth kernel or $\pm I$, let $T_{2}$  and $T_{4}$ be the linear operators and  let $T_{3}=\pm I$. Denote the Toeplitz type operator by$$T^b=T_{1}M^bI_\alpha T_{2}+T_{3}I_\alpha M^b T_{4},$$where $M^bf=bf,$ and $I_\alpha$ is the fractional integral operator. In this paper, we investigate the boundedness of the operator $T^b$ on the weighted Morrey space when $b$ belongs to the weighted BMO space.