On Hardy spaces in complex ellipsoids

Abstract

This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space H 1 . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define H 1 with respect to a certain measure that degenerates near Levi-flat points and is closely related to explicit representation formulas for holomorphic functions. For the model domain B p =z ∈ ℂ n : ∑ j=1 n | z j | 2p j ≤ 1,p j ∈ℤ + , both atomic decomposition and factorization of H 1 -functions are established. The duality between H 1 and BMOA is also considered.