Multilinear Calderon-Zygmund operators on Hardy spaces, II

In this note we explain a point left open in the literature of Hardy spaces, namely that for a sufficiently smooth m-linear Calderon-Zygmund operator bounded on a product of Lebesgue spaces we have T(f(1), ..., f(m)) = Sigma(i1) ...Sigma (im) lambda 1, i(1) ... lambda m,i(m) T(a1,i(1,...),a(m,)i(m)) a.e., where aj,i, are H-pj atoms, lambda j,i(j) is an element of C, and f(j) = Sigma(ij) lambda j,i(j) aj,i(j) are H-pj distributions. In some particular cases the proof is new even when m = 1. (C) 2014 Elsevier Inc. All rights reserved.