Boundedness of Forelli-Rudin Type Operators on Tubular Domains over The Generalized Light Cones

Abstract

This study investigates conditions for the boundedness of Forelli-Rudin type operators on weighted Lebesgue spaces associated with tubular domains over the generalized light cone. We establish a complete characterization of the boundedness for two classes of Forelli-Rudin type operators from $L_{\mathbf{\alpha }}^p$ to $L_{\mathbf{\beta }}^q$, in the range $1<p\le q<\infty$. The findings contribute significantly to the analysis of Bergman projection operators in this setting.