Lp boundedness of Marcinkiewicz integral operators

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