Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces

Abstract

Let $T$ be the singular integral operator with variable kernel, $T^*$ be the adjoint of $T$ and $T^{\sharp}$ be the pseudo-adjoint of $T$. Let $T_1T_2$ be the product of $T_1$ and $T_2,$ $T_1\circ T_2$ be the pseudo product of $T_1$ and $T_2.$ In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator $D^\gamma$ on the weighted Morrey spaces.