Boundedness of a class of rough maximal functions

In this work, we obtain appropriate sharp bounds for a certain class of maximal operators along surfaces of revolution with kernels in Lq( Sn- 1), q > 1. By using these bounds and using an extrapolation argument, we establish the Lp boundedness of the maximal operators when their kernels are in L( log L) a( Sn- 1) or in the block space B0, a- 1 q ( Sn- 1). Our main results represent significant improvements as well as natural extensions of what was known previously.