$L^{\vec{p}}-L^{\vec{q}}$ Boundedness of Multiparameter Forelli-Rudin Type Operators on Tube Domains Over The Forward Light Cones

TL;DR

This paper characterizes the boundedness of multiparameter Forelli-Rudin operators on weighted Lebesgue spaces over tube domains related to the forward light cone, advancing understanding of Bergman projections in this geometric context.

Contribution

It provides a complete characterization of boundedness conditions for these operators between mixed-norm Lebesgue spaces, extending prior results to multiparameter and geometric settings.

Findings

Established necessary and sufficient conditions for boundedness.

Characterized boundedness for two classes of operators.

Enhanced understanding of Bergman projections on tube domains.

Abstract

This study investigates necessary and sufficient conditions for the boundedness of Forelli-Rudin type operators on weighted Lebesgue spaces associated with tubular domains over the forward light cone. We establish a complete characterization of the boundedness for two classes of multiparameter Forelli-Rudin type operators from the mixed-norm Lebesgue space $L^{\vec{p}}$ to $L^{\vec{q}}$, in the range $1 \leq \vec{p} \leq \vec{q} < \infty$. The findings contribute significantly to the analysis of Bergman projection operators in this setting.