The Commutators of Marcinkiewicz Integral Operators on Weighted Hardy Spaces

Abstract

This paper is devoted to studying the behaviors of commutator μΩb generated by the Marcinkiewicz integral μΩ with b ∈ BMO(ℝn) on the weighted Hardy spaces. The authors show that there is a non-trivial subspace of BMO(ℝn), when b belongs to this subspaces, such that μΩb is bounded from the weighted Hardy spaces H (ℝn) to the weighted Lebesgue spaces L (ℝn) for some 0 < p ≤ 1.