Formula omitted] boundedness of Marcinkiewicz integral operators

Abstract

In this paper we prove the L p boundedness of Marcinkiewicz integral operators associated to compact submanifolds of finite type under the L ( log L ) 1 / 2 condition on the kernel functions. The exponent 1/2 is optimal. We also show that the L p boundedness may fail to hold if the underlying submanifold is not required to be of finite type.