Weak factorization and Hankel forms for weighted Bergman spaces on the unit ball

TL;DR

This paper develops weak factorizations for weighted Bergman spaces on the unit ball in complex space and characterizes bounded Hankel forms, advancing understanding of function space decompositions and operator boundedness.

Contribution

It introduces new weak factorization results for weighted Bergman spaces and provides a characterization of bounded Hankel forms on these spaces.

Findings

Established weak factorizations for $A^p_{eta}$ spaces.

Characterized bounded Hankel forms on weighted Bergman spaces.

Extended factorization techniques to higher-dimensional complex spaces.

Abstract

We establish weak factorizations for a weighted Bergman space $A^p_{\a}$, with $1<p<\infty$, into two weighted Bergman spaces on the unit ball of $\C^n$. To obtain this result, we characterize bounded Hankel forms on weighted Bergman spaces on the unit ball of $\C^n$.