Weighted <i>L^p</i> boundedness of maximal operators with rough kernels

Abstract

In this paper, we study the weighted spaces $ L^p(\omega, \mathbb{R}^d) $ boundedness of certain class of maximal operators when their kernels belong to the space $ L^{q}(\mathbb{S} ^{d-1}) $, $ q > 1 $. Our results in this paper are improvements and extensions of some previously known results.

Keywords

• maximal functions
• $ l^p $ boundedness
• rough kernels
• surfaces of revolution
• extrapolation