Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space (Analysis in Theory and Applications, 2017)
Let $T_{1}$ be a singular integral with non-smooth kernel or $± I$, let $T_{2}$ and $T_{4}$ be the linear operators and let $T_{3}=± I$. Denote the Toeplitz type operator by$$T^b=T_{1}M^bI_α T_{2}+T_{3}I_α M^b T_{4},$$where $M^bf=bf,$ and $I_α$ 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.
Keywords: Toeplitz operator; non-smooth kernel; weighted BMO; fractional integral; weighted Morrey space.