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

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.