Bilinear operators on Herz-type Hardy spaces

The authors prove that bilinear operators given by finite sums of products of Calderon-Zygmund operators on R-n are bounded from H(K) over dot (alpha 1,p1)(q1) x H(K) over dot (alpha 2,p2)(q2) into H(K) over dot (alpha,p)(q) if and only if they have vanishing moments upto a certain order dictated by the target space. Here H(K) over dot (alpha,p)(q) homogeneous Herz-type Hardy spaces with 1/p = 1/p(1) + 1/p(2), 0 < p(i) less than or equal to infinity, 1/q = 1/q(1) + 1/q(2), 1 < q(1),q(2) < infinity, 1 less than or equal to q < infinity, alpha = alpha(1) + alpha(2) and -n/q(i) < alpha(i) < infinity. As an application they obtain that the commutator of a Calderon-Zygmund operator with a BMO function maps a Herz space into itself.