Marcinkiewicz integrals with rough kernels in H^(1)(s^(n-1))

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 byΩ∈H^(1)(s^(n-1))and h∈Δ_(γ)(R_(+))for someγ>1.It should be pointed out that the bounds are independent of h,Ω,γ,and the coefficients of the polynomials in the definition of the operators.