Small weighted Bergman spaces

TL;DR

This survey reviews recent advances in the theory of weighted Bergman spaces $A^p_ ho$, focusing on spaces induced by radial weights with the doubling property, highlighting new theoretical developments.

Contribution

It presents recent progress on the theory of weighted Bergman spaces with radial weights satisfying the doubling condition, expanding understanding of their structure and properties.

Findings

Progress in characterizing weighted Bergman spaces with doubling weights

New results on the structure of $A^p_ ho$ spaces

Enhanced understanding of radial weight conditions

Abstract

This paper is based on the course \lq\lq Weighted Hardy-Bergman spaces\rq\rq\, I delivered in the Summer School \lq\lq Complex and Harmonic Analysis and Related Topics\rq\rq at the Mekrij\"arvi research station of University of Eastern Finland, June $2014$. The main purpose of this survey is to present recent progress on the theory of Bergman spaces $A^p_\omega$, induced by radial weights $\omega$ satisfying the doubling property $\int_r^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$.