Some Hilbert Spaces related with the Dirichlet space
Nicola Arcozzi, Karl-Mikael Perfekt, Pavel Mozolyako, Stefan Richter,, Giulia Sarfatti

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 , where is a positive integer and is the reproducing kernel of the analytic Dirichlet space.
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