In this paper, we prove the $L^p$ boundedness of generalized Marcinkiewicz operators along surfaces of revolution on product spaces under very weak conditions on the the singular kernels. Our results generalize and improve many previously known results.

In this paper, we study the weighted spaces $L^p(\omega ,{\mathbb{R}}^d)$ boundedness of certain class of maximal operators when their kernels belong to the space $L^q({\mathbb{S}}^{d-1})$, $q>1$. Our results in this paper are improvements and extensions of some previously known results.