On rough maximal operators and Marcinkiewicz integrals along submanifolds

Abstract

We investigate the LP boundedness for a class of parametric Marcinkiewicz integral operators associated to submanifolds and a class of related maximal operators under the L(log L)α(Sn-1) condition on the kernel functions. Our results improve and extend some known results. © Instytut Matematyczny PAN, 2009.