Contractive multipliers from Hardy space to weighted Hardy space

TL;DR

This paper demonstrates how contractive multipliers from Hardy space to weighted Hardy space can be factored through Schur multipliers, leading to new insights in interpolation within these function spaces.

Contribution

It introduces a factorization method for contractive multipliers into classical Schur multipliers and applies this to interpolation problems in Hardy and weighted Hardy spaces.

Findings

Factorization of contractive multipliers into Schur multipliers.

New results on interpolation for Hardy-to-weighted-Hardy multipliers.

Enhanced understanding of multiplier structures in Hardy spaces.

Abstract

It is shown how any contractive multiplier from the Hardy space to a weighted Hardy space $H^{2}_{\bbeta}$ can be factored as a fixed factor composed with the classical Schur multiplier (contractive multiplier between Hardy spaces). The result is applied to get results on interpolation for a Hardy-to-weighted-Hardy contractive multiplier class.