Integral Transforms Connecting the Hardy space with Barut-Girardello Spaces

TL;DR

This paper introduces a family of integral transforms that establish a connection between the Hardy space and Barut-Girardello weighted Bergman spaces, expanding the tools for analyzing these function spaces.

Contribution

It constructs a one-parameter family of integral transforms linking Hardy space with Barut-Girardello spaces, a novel connection in functional analysis.

Findings

Established a new integral transform connecting Hardy and Barut-Girardello spaces

Provided a parameterized family of transforms for flexible analysis

Enhanced understanding of relationships between classical and weighted spaces

Abstract

We construct a one parameter family of integral transforms connecting the classical Hardy space with a class of weighted Bergman spaces called Barut-Girardello spaces.