On the boundedness of a class of rough maximal operators on product spaces

Abstract

In this paper, we study the L^p boundedness of a class of maximal operators T_{Ωj}^(γ) and a related class of rough singular integrals on product spaces. We obtain appropriate L^p estimates for such maximal operators and singular integrals. These estimates are used in an extrapolation argument and allow us to obtain some new and improved results for certain maximal integral operators and singular integrals on product spaces under certain sharp conditions on the kernel functions. Also, one of our main results in this paper is a corrigendum of a result obtained by Ding-Lin.