Multilinear Calderón–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 Calderón–Zygmund operator bounded on a product of Lebesgue spaces we haveT(f1,…,fm)=∑i1⋯∑imλ1,i1⋯λm,imT(a1,i1,…,am,im)a.e., where aj,ij are Hpj atoms, λj,ij∈C, and fj=∑ijλj,ijaj,ij are Hpj distributions. In some particular cases the proof is new even when m=1.