$L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space

TL;DR

This paper characterizes the conditions under which Bergman-type operators are bounded between different L^p and L^q spaces over the Siegel upper half-space, extending previous results to higher dimensions.

Contribution

It generalizes the known $L^p-L^q$ boundedness criteria for Bergman-type operators to higher-dimensional Siegel upper half-spaces.

Findings

Established $L^p-L^q$ boundedness conditions for Bergman-type operators

Extended previous results to higher dimensions

Provided a comprehensive characterization of operator boundedness

Abstract

We characterize the $L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans. Amer. Math. Soc. 369:8643--8662, 2017) to higher dimensions.