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

L p estimates for maximal functions along surfaces of revolution on product spaces