Norm estimates for the Bergman and Cauchy-Szegö projections over the Siegel upper half-space

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.