A unifying approach for certain class of maximal functions

We establish Lp estimates for certain class of maximal functions with kernels in Lq ( S n-1). As a consequence of such Lp estimates, we obtain the Lp boundedness of our maximal functions when their kernels are in L( logL) 1/2 ( S n-1) or in the block space Bq 0,-1/2 ( S n-1), q>1. Several applications of our results are also presented.