Invariant metrics and the boundary behavior of holomorphic functions on domains in $$\mathbb{C}^n $$

Abstract

Invariant metrics are used to provide a unified approach to the study of holomorphic functions in Hardy classes on domains in one and several complex variables. Both approach regions and boundary measures are constructed from the metric. Examples are provided to show how diverse theories can be unified with this approach. The Hartogs extension phenomenon and Fatou’s theorem are seen to be two aspects of the same circle of ideas.