Boundedness for Multilinear Littlewood-Paley Operators on Hardy and Herz-Hardy Spaces

Let T be a Calderon-Zygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T ] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator. However, it was observed that [b, T ] is not bounded, in general, from Hp(Rn) to Lp(Rn) for p ≤ 1. But, the boundedness holds if b belongs to Lipschitz spaces Lipβ(R) (see [3],[15]). This shows the difference of b ∈ BMO(Rn) and b ∈ Lipβ(R). The purpose of this paper is to prove the boundedness properties for some multilinear operators generated by Littlewood-Paley operators and Lipschitz functions on Hardy and Herz-Hardy spaces.