Degenerate elliptic operators, Hardy spaces and diffusions on strongly pseudoconvex domains (Q1345466)

The author investigates linear topological properties of the Hardy space \(H^ 1\) associated to solutions of the Laplace-Beltrami operator and more general elliptic operators on a smoothly bounded strongly pseudoconvex domain equipped with the Bergman metric. He characterizes such Hardy spaces in terms of diffusions and non-isotropic atoms, sees that the dual space of \(H^ 1\) is equivalent to the nonisotropic BMO space, sees that \(H^ 1\) is isomorphic to the classical Hardy space on the open unit disc in the plane and proves that the Hardy space \(H^ 1\) of holomorphic functions on a strongly pseudoconvex domain is isomorphic to the classical one on the open unit disc, as conjectured by Wotjaszczyk.