Forelli–Rudin-type operators on tube domains over the realification of the Siegel upper half-space

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发表日期：

2026年3月25日

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Jiaxin Liu,
Guan-Tie Deng

摘要

We introduce the realification of the Siegel upper half-space, a domain in real space obtained by treating the real and imaginary parts of each complex coordinate as independent variables. On the tube domain over this realified space, we derive an explicit formula for the weighted Bergman kernel and establish necessary and sufficient conditions for the boundedness of two classes of Forelli–Rudin-type operators acting between weighted $L^p$ $L^{p}$ and $L^q$ $L^{q}$ spaces for all $(p,q)\in [1,\infty ]\times [1,\infty ]$ $(p, q) \in [1, \infty] \times [1, \infty]$ .