Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces

Abstract

Similar to the property of a linear Calderón-Zygmund operator, a linear fractional type operator I_α associated with a BMO function b fails to satisfy the continuity from the Hardy space H^p into L^p for p≤1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b, I_α] is continuous from an atomic Hardy space H_b^p into L^p,where H_b^p is a subspace of the Hardy space H^p for n/(n+1)<p≤1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint (H_{b\mathrm{1}}^{p\mathrm{1}}\times \cdots \times H_{bm}^{pm}, L^p) boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderón-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b\in {(\mathrm{L}\mathrm{i}{\mathrm{p}}_{\beta })}^m({ℝ}^n).

Key words： Multilinear fractional type operator; multilinar Calderón-Zygmund operator; commutator; Hardy type space

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