An extremality property of Szeg\H{o} projections on Heisenberg groups

TL;DR

This paper demonstrates that Heisenberg groups uniquely minimize the $L^p$ operator norm of the Szeg ext{"o} projection among a broad class of weighted CR manifolds of hypersurface type, highlighting their extremal geometric property.

Contribution

It establishes a new extremality property of Heisenberg groups as minimizers of the Szeg ext{"o} projection norm in weighted CR manifolds.

Findings

Heisenberg groups minimize the $L^p$ operator norm of the Szeg ext{"o} projection.

This extremality holds in a large class of weighted CR manifolds.

The result links geometric structure with operator norm minimization.

Abstract

We prove that Heisenberg groups, a.k.a. the boundaries of Siegel domains, minimize the $L^p$ operator norm of the Szeg\H{o} projection in a large class of weighted CR manifolds of hypersurface type.