Degenerate elliptic operators, hardy spaces and diffusions on strongly pseudoconvex domains

We will study some linear topological properties of Hardy space H¹ associated to solutions of the Laplace-Beltrami operator or more general elliptic operators on a smoothly bounded strongly pseudoconvex domain endowed with the Bergman metric. In particular, we characterize such Hardy spaces in terms of diffusions and non-isotropic atoms. Consequently we see that the dual space of H¹ is equivalent to the non-isotropic BMO space and that H¹ is isomorphic to the classical Hardy space on the open unit disc in the plane. As a corollary we also prove that the Hardy space H¹ of holomorphic functions on a strongly pseudoconvex domain is isomorphic to the classical one on the open unit disc, as conjectured by P. Wojtaszczyk.