Some Hilbert Spaces related with the Dirichlet space

TL;DR

This paper explores a class of Hilbert spaces associated with the Dirichlet space by examining their reproducing kernels, aiming to understand their structure and properties.

Contribution

It introduces and studies a new family of Hilbert spaces related to the Dirichlet space through their reproducing kernels, expanding the theoretical understanding of these spaces.

Findings

Characterization of the reproducing kernel for the new Hilbert spaces

Analysis of the space's properties related to the Dirichlet space

Initial insights into the structure of these Hilbert spaces

Abstract

We do a preliminary study of the reproducing kernel Hilbert space having as kernel $k^d$, where $d$ is a positive integer and $k$ is the reproducing kernel of the analytic Dirichlet space.