Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type

Abstract

In this article, we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. The weight $\omega$ considered here belongs to the Muckenhoupt’s class $A_∞.$ Moreover, weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.