The boundedness of integral operators of Forelli–Rudin type on the Hartogs triangle

We completely characterize Lp-Lq boundedness of integral operators of Forelli–Rudin type acting on the Hartogs triangle H={(z1,z2)∈C2:|z1|<|z2|<1} for all 1≤p,q≤∞, which generalizes the characterization of Lp-Lq boundedness on the unit ball given by Zhao and Zhou [J. Funct. Anal. 282 (2022)]. Due to the non-smooth boundary of the Hartogs triangle, our strategies are essentially different than in the case of unit ball. As an application, we also study the hyper-singular property of Bergman-type operators, which gives a positive answer to the conjecture raised by Cheng et al. [Trans. Amer. Math. Soc. {369} (2017)] for the Hartogs triangle setting.