Parametric Marcinkiewicz integrals on weighted Hardy and weak Hardy spaces

Abstract

Let $0<\rho<n$ and $\mu^{\rho}_{\Omega}$ be the parametric Marcinkiewicz integral. In this paper, by using the atomic decomposition theory of weighted Hardy and weak Hardy spaces, we will obtain the boundedness properties of $\mu^{\rho}_\Omega$ on these spaces, under the Lipschitz condition imposed on the kernel $\Omega$.