Boundedness of Commutators for Marcinkiewicz Integrals on Weighted Herz-Type Hardy Spaces

Abstract

In this paper, the authors study the boundedness of the operator $\mu^b_\Omega$, the commutator generated by a function $b \in \text{Lip}_\beta (\mathbf{R}^n)$ $(0<\beta<1)$ and the Marcinkiewicz integral $\mu_\Omega$ on weighted Herz-type Hardy spaces.