Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces

In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M-Omega,phi,h,rho((r)) is considered. Under the condition that Omega is a function in L-q(Sn-1) with q is an element of(1,2], appropriate estimates of the aforementioned operators from Triebel-Lizorkin spaces to L-p spaces are obtained. By these estimates and an extrapolation argument, we establish the boundedness of such operators when the kernel function Omega belongs to the block space B-q(0,nu-1)(Sn-1) or in the space L(logL)(nu)(Sn-1). Our results represent improvements and extensions of some known results in generalized parametric Marcinkiewicz integrals.