Bloch type spaces on the unit ball of a Hilbert space

TL;DR

This paper introduces Bloch type spaces on the unit ball of a Hilbert space, exploring their properties and applications, including an infinite-dimensional Hardy-Littlewood theorem and characterizations of related holomorphic function spaces.

Contribution

It initiates the study of Bloch type spaces in infinite-dimensional Hilbert spaces and provides new theorems and characterizations related to these spaces.

Findings

Hardy-Littlewood theorem extended to infinite-dimensional Hilbert spaces

Characterizations of holomorphic function spaces related to Bloch type spaces

Foundational framework for Bloch type spaces in infinite dimensions

Abstract

In this article, we initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented.