Boundary Values Properties of Functions in Weighted Hardy Spaces

Abstract

In this paper we study the boundary values of harmonic and holo- morphic functions in the weighted Hardy spaces on the unit disk $\mathbb{D}$. These spaces were introduced by Poletsky and Stessin in [6] for plurisubharmonic functions on hyperconvex domains $D\subset {\mathbb{C}}^n$ as generalizations of classical Hardy spaces. We show that in the case when $D$ is the unit disk $\mathbb{D}$ the theory of boundary values for functions in these spaces is analogous to the classical one.

13 pages

Cited by in corpus (2)

• Weighted Hardy spaces on the unit disk
• Projective limits of Poletsky--Stessin Hardy spaces