A Littlewood-Paley type theorem for Bergman spaces

TL;DR

This paper extends the Littlewood-Paley theory to Bergman spaces, showing that the classical $g$-functions can characterize these spaces similarly to their role in other function spaces.

Contribution

It introduces a Littlewood-Paley type theorem for Bergman spaces, establishing a new characterization method using $g$-functions.

Findings

Littlewood-Paley $g$-functions characterize Bergman spaces

Extension of classical harmonic analysis tools to complex analysis

New analytical framework for Bergman space theory

Abstract

In this paper, we prove that the original Littlewood-Paley $g$-functions can be used to characterize Bergman spaces as well.