Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 56272, 17 pages
doi:10.1155/JIA/2006/56272

A unifying approach for certain class of maximal functions

Ahmad Al-Salman

Department of Mathematics, Faculty of Science, Yarmouk University, Irbid, Jordan

Received 16 January 2006; Revised 12 April 2006; Accepted 13 April 2006

Copyright © 2006 Ahmad Al-Salman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish Lp estimates for certain class of maximal functions with kernels in Lq(Sn−1). As a consequence of such Lp estimates, we obtain the Lp boundedness of our maximal functions when their kernels are in L(log⁡L)1/2(Sn−1) or in the block space Bq0,−1/2(Sn−1), q>1. Several applications of our results are also presented.