Hadamard multipliers on weighted Dirichlet spaces

TL;DR

This paper characterizes Hadamard multipliers on weighted Dirichlet spaces with superharmonic weights, providing sharp norm estimates and applications like an analogue of Fejér's theorem and new bounds for weighted Dirichlet integrals.

Contribution

It offers a complete characterization of Hadamard multipliers on these spaces and establishes sharp estimates for their norms, advancing understanding of their structure and applications.

Findings

Characterization of Hadamard multipliers on weighted Dirichlet spaces

Sharp estimates for multiplier norms

Applications to Fejér's theorem and Dirichlet integral bounds

Abstract

The Hadamard product of two power series is obtained by multiplying them coefficientwise. In this paper we characterize those power series that act as Hadamard multipliers on all weighted Dirichlet spaces on the disk with superharmonic weights, and we obtain sharp estimates on the corresponding multiplier norms. Applications include an analogue of Fej\'er's theorem in these spaces, and a new estimate for the weighted Dirichlet integrals of dilates.