Bilinear operators on Herz-type Hardy spaces

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on R n \mathbb {R}^{n} are bounded from H K ˙ q 1 α 1 , p 1 × H K ˙ q 2 α 2 , p 2 H\dot K_{q_{1}}^{\alpha _{1},p_{1}}\times H\dot K_{q_{2}}^{\alpha _{2},p_{2}} into H K ˙ q α , p H\dot K_{q}^{\alpha ,p} if and only if they have vanishing moments up to a certain order dictated by the target space. Here H K ˙ q α , p H\dot K_{q}^{\alpha ,p} are homogeneous Herz-type Hardy spaces with 1 / p = 1 / p