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 ^p _b into L ^p, where H ^p _b 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 $(H_{b_1 }^{p_1 } \times \cdots \times H_{bm}^{p_m } ,L^p )$ 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 ∈ (Lip _β )^m(ℝⁿ).