The corona theorem in weighted Hardy and Morrey spaces

TL;DR

This paper provides a unified proof of the corona theorem for weighted Hardy and Morrey spaces, utilizing a technique that reduces the problem to Hardy spaces, thereby advancing understanding in complex analysis.

Contribution

It introduces a novel unified approach to prove the corona theorem across weighted Hardy and Morrey spaces, connecting these spaces through a reduction technique.

Findings

Unified proof of the corona theorem for weighted Hardy and Morrey spaces

Reduction of the problem to Hardy spaces $H^2( heta)$

Enhanced understanding of function theory in complex spaces

Abstract

The main goal of this paper is to give an unified proof of the corona problem on weighted Hardy spaces and on Morrey spaces. We use a technique that allows to reduce the problem to the Hardy spaces $H^2(\theta)$