Boundedness for a Class of Operators on Weighted Morrey Space with RD-Measure

Abstract

In this paper, we study a class of sublinear operators and their commutators with a weighted BMO function. We first give the definition of a weighted Morrey space $L^{p,\kappa}_{\mu,\omega}(X)$ where $X$ is an RD-measure and $\omega$ is the weight function. The weighted Morrey spaces arise from studying the local behavior of solutions to certain partial differential equations. We will show that the aforementioned class of operators and their communtators with a weighted BMO function are bounded in the weighted Morrey space $L^{p,\kappa}_{\mu,\omega}(X)$ provided that the weight function $\omega$ belongs to the $A_p(\mu)$-class and satisfies the reverse Hölder's condition.