Lp estimates for maximal functions along surfaces of revolution on product spaces

This paper is concerned with establishing Lp estimates for a class of maximal operators associated to surfaces of revolution with kernels in Lq(Sn−1 × Sm−1), q > 1. These estimates are used in extrapolation to obtain the Lp boundedness of the maximal operators and the related singular integral operators when their kernels are in the L(logL)κ(Sn−1 × Sm−1) or in the block space Bq0,κ−1$\begin{array}{} B^{0,\kappa-1}_ q \end{array}$(Sn−1 × Sm−1). Our results substantially improve and extend some known results