BOUNDEDNESS OF MONGE-AMPERE SINGULAR INTEGRAL OPERATORS ACTING ON HARDY SPACES AND THEIR DUALS

We study the Hardy spaces H-J(p) associated with a family F of sections which is closely related to the Monge-Ampere equation. We characterize the dual spaces of H-F(p), which can be realized as Carleson measure spaces, Campanato spaces, and Lipschitz spaces. Also the equivalence between the characterization of the Littlewood-Paley g-function and atomic decomposition for H-F(p) is obtained. Then we prove that Monge-Ampere singular operators are bounded from H-F(p) into L-mu(p) and bounded on both H-F(p) and their dual spaces.