On certain rough integral operators and extrapolation

Abstract

In this paper, we obtain sharp Lp estimates of two classes of maximal operators related to rough singular integrals and Marcinkiewicz integrals. These estimates will be used to obtain similar estimates for the related singular integrals and Marcinkiewicz integrals. By the virtue of these estimates and extrapolation we obtain the Lp boundedness of all the aforementioned operators under rather weak size conditions. Our results represent significant improvements as well as natural extensions of what was known previously. © 2009 Victoria University. All rights reserved.