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

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.