Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound

TL;DR

This paper establishes new two-sided norm estimates for Bergman-type projections with standard weights, providing asymptotically sharp bounds and insights into a recent conjecture in the field.

Contribution

It introduces novel two-sided norm estimates for weighted Bergman projections and computes the exact norm of the maximal Bergman projection, advancing understanding of their asymptotic behavior.

Findings

Lower bound asymptotically matches Riesz projection norm as alpha approaches -1

Exact operator norm of the maximal Bergman projection is calculated

Results support a recent conjecture on Bergman projection norms

Abstract

We obtain new two-sided norm estimates for the family of Bergman-type projections arising from the standard weights $(1-|z|^2)^{\alpha}$ where $\alpha>-1$. As $\alpha\to -1$, the lower bound is sharp in the sense that it asymptotically agrees with the norm of the Riesz projection. The upper bound is estimated in terms of the maximal Bergman projection, whose exact operator norm we calculate. The results provide evidence towards a conjecture that was posed very recently by the first author.