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

Similar to the property of a linear Calderón-Zygmund operator, a linear fractional type operator Iα associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ⩽ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b, Iα] is continuous from an atomic Hardy space Hbp into Lp, where Hbp is a subspace of the Hardy space Hp 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(H_{b_1 }^{p_1 } \times \cdots \times H_{bm}^{p_m } ,L^p )$\end{document} 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 ∈ (Lipβ)m(ℝn).