Maximal operators related to block spaces

Abstract

In this paper, we prove appropriate L^p bounds for a class of maximal operators \mathscr{S}_Ω related to singular integrals with kernels which belong to block spaces and are supported by subvarieties. Also, we show that our condition on the kernel is optimal for the L² boundedness of \mathscr{S}_Ω. Our results improve substantially the main result obtained by L. K. Chen and H. Lin in [CL].