Parametric Marcinkiewicz integrals on weighted Hardy and weak Hardy spaces

Abstract

Let $0<\rho <n$ and ${\mu }_{\Omega }^{\rho }$ 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 ${\mu }_{\Omega }^{\rho }$ on these spaces, under the Lipschitz condition imposed on the kernel $\Omega$.

17 pages. arXiv admin note: substantial text overlap with arXiv:1111.4269, arXiv:1103.1821, arXiv:1207.1242, arXiv:1010.0862