Estimates of the $L^p$ norms of the Bergman projection on strongly pseudoconvex domains

TL;DR

This paper provides estimates for the $L^p$ norms of the Bergman projection on strongly pseudoconvex domains, showing they are comparable to $rac{p^2}{p - 1}$ for all $p$ in $(1, \, \infty)$, advancing understanding of operator bounds.

Contribution

It establishes a precise asymptotic estimate for the $L^p$ norm of the Bergman projection on strongly pseudoconvex domains, a significant step in complex analysis.

Findings

The $L^p$ norm of the Bergman projection is comparable to $rac{p^2}{p - 1}$.

The estimate holds uniformly for all $p$ in $(1, \infty)$.

This result improves understanding of the boundedness properties of the Bergman projection.

Abstract

We give estimates of the $L^p$ norm of the Bergman projection on a strongly pseudoconvex domain in $\mathbb{C}^n$. We show that this norm is comparable to $\frac{p^2}{p - 1}$ for $1 <p< \infty$.