Marcinkiewicz integrals with rough kernels in H~1(S~(n-1))

摘要

This paper is devoted to studying the Marcinkiewicz integral operators associated to polynomial compound curves. Some new bounds for the above operators on the Lebesgue, Triebel-Lizorkin, and Besov spaces are established by assuming that their rough kernels are given by omega is an element of H-1 (Sn-1) and h is an element of Delta(gamma) (DOUBLE-STRUCK CAPITAL R+) for some gamma 1. It should be pointed out that the bounds are independent of h, omega, gamma, and the coefficients of the polynomials in the definition of the operators.