On weighted Hardy spaces on the unit disk

TL;DR

This paper characterizes weighted Hardy spaces that are Poletsky–Stessin Hardy spaces on the unit disk, offering a reduction method to simplify complex analysis problems like interpolation and corona problems.

Contribution

It provides a complete characterization of weighted Hardy spaces as Poletsky–Stessin spaces and introduces a reduction technique for $H^$ problems to $H^p_u$ problems.

Findings

Complete characterization of weighted Hardy spaces as Poletsky–Stessin spaces

Reduction of $H^$ problems to $H^p_u$ problems

Simplified proofs for interpolation and corona theorems

Abstract

In this paper we completely characterize those weighted Hardy spaces that are Poletsky--Stessin Hardy spaces $H^p_u$. We also provide a reduction of $H^\infty$ problems to $H^p_u$ problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.