$L^{\vec{p}}-L^{\vec{q}}$ Boundedness of Multiparameter Forelli-Rudin Type Operators on the Siegel Upper Half-space

TL;DR

This paper characterizes the boundedness conditions for multiparameter Forelli-Rudin type operators between weighted mixed-norm Lebesgue spaces on the Siegel upper half-space, advancing understanding of their functional analysis properties.

Contribution

It provides necessary and sufficient conditions for the boundedness of these operators, a novel result in the context of multiparameter analysis on the Siegel upper half-space.

Findings

Established exact boundedness criteria for the operators.

Extended classical results to multiparameter and weighted settings.

Enhanced understanding of operator behavior in complex analysis contexts.

Abstract

In this article,we present exactly when two classes of multiparameter Forelli-Rudin type integral operators are bounded from one weighted mixed-norm Lebesgue space $L^{\vec{p}}$ to another space $L^{\vec{q}}$ over the Siegel upper half-space.