Duality and Interpolation of Bergman Spaces

TL;DR

This paper investigates the duality and interpolation properties of p-Bergman spaces, establishing conditions under which dual spaces are q-Bergman spaces and comparing domain properties.

Contribution

It provides new insights into the duality and interpolation of Bergman spaces, linking duality with domain regularity and integrability conditions.

Findings

Identifies conditions for dual spaces to be q-Bergman spaces

Analyzes the interpolation space of a Banach couple in this context

Draws comparisons between duality, integrability, and regularity properties

Abstract

This paper explores the dual space corresponding to p-Bergman space and examines the essential condition for the dual space to be a q-Bergman space. The investigation involves a detailed examination of the interpolation space of a Banach couple. Additionally, we draw comparisons between the `duality', `integrability' and `regularity' properties of a domain.