Weighted L ^p Boundedness of Marcinkiewicz Integral

Abstract.

A weighted norm inequality for the Marcinkiewicz integral operator $\mu_{\Omega}$ is proved when Ω belongs to $H^1(S^{n-1}), n \geq 2$. We also give the weighted L ^p-boundedness for a class of Marcinkiewicz integral operators with rough kernels $\mu^{*}_{\Omega, \lambda}$ and $\mu_{\Omega, S}$ related to the Littlewood-Paley $g^{*}_{\lambda}$-function and the area integral S, respectively.