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 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 Hbp into L^p,where Hbp 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 (Hb1p1×?×Hbmpm, 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∈(Lipβ)m(?n).