Norm estimates for the Bergman and Cauchy-Szeg\"o projections over the Siegel upper half-space

TL;DR

This paper provides precise $L^p$ operator norm estimates for the Bergman and Cauchy-Szeg"o projections on the Siegel upper half-space, advancing understanding of their boundedness and operator behavior.

Contribution

It establishes exact $L^p$ operator norms for these projections and related integral operators on the Siegel upper half-space, a novel contribution in several complex variables.

Findings

Derived $L^p$ bounds for Bergman and Cauchy-Szeg"o projections.

Determined exact operator norms for a family of integral operators.

Enhanced understanding of projection operators in complex analysis.

Abstract

We obtain several estimates for the $L^p$ operator norms of the Bergman and Cauchy-Szeg\"o projections over the the Siegel upper half-space. As a by-product, we also determine the precise value of the $L^p$ operator norm of a family of integral operators over the Siegel upper half-space.