A characterization of Dirichlet-inner functions

TL;DR

This paper introduces a new class of inner functions tailored for Dirichlet-type spaces, providing a characterization based on norm equalities that enhances understanding of their structure.

Contribution

It offers a novel characterization of Dirichlet-inner functions through the equality of space and multiplier norms, advancing the theoretical framework of Dirichlet spaces.

Findings

Dirichlet-inner functions characterized by norm conditions

Equality of space and multiplier norms for these functions

Enhanced understanding of Dirichlet space structure

Abstract

We study a concept of inner function suited to Dirichlet-type spaces. We characterize Dirichlet-inner functions as those for which both the space and multiplier norms are equal to 1.