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

TL;DR

This paper characterizes when Forelli-Rudin type operators are bounded on weighted Lebesgue spaces over tubular domains related to generalized light cones, advancing the understanding of Bergman projections in this geometric context.

Contribution

It provides a complete characterization of boundedness conditions for two classes of Forelli-Rudin type operators on these specialized domains.

Findings

Boundedness conditions are fully characterized for the operators.

Results apply to operators from $L_{\boldsymbol{\alpha}}^{p}$ to $L_{\boldsymbol{\beta}}^{q}$.

Enhances analysis of Bergman projection operators in tubular domains.

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 $L_{\boldsymbol{\alpha}}^{p}$ to $L_{\boldsymbol{\beta}}^{q}$, in the range $1 < p \leq q < \infty$. The findings contribute significantly to the analysis of Bergman projection operators in this setting.