A note on Fefferman-Stein type characterizations for certain spaces of analytic functions in the unit disk

TL;DR

This paper provides new characterizations of Bergman and Bloch spaces in the unit disk using equivalent (quasi)-norms, inspired by Fefferman and Stein's estimates for Hardy spaces in R^n.

Contribution

It introduces novel (quasi)-norm characterizations of Bergman and Bloch spaces, extending Fefferman-Stein type estimates to these analytic function spaces.

Findings

New (quasi)-norm characterizations of Bergman spaces

Equivalent norms for Bloch spaces

Extension of Fefferman-Stein estimates to analytic spaces

Abstract

We obtain new characterizations of Bergman and Bloch spaces on the unit disc involving equivalent (quasi)-norms of these spaces.Our results are in spirit of estimates obtained by Fefferman and Stein for HArdy spaces in R^n.