Boundedness of maximal functions in Lp spaces

Abstract

In this paper, we derive suitable L^p bounds for a specific class of maximal operators defined along the surface of revolution, where the kernels belong to L^q(S^n-1) with q > 1. Using these bounds in conjunction with extrapolation techniques, we establish the L^p boundedness of the maximal operator when its kernels lie in the block space B_q^{(0, s-1)}(S^n-1) or in (L log L)^s(S^n-1).