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

We completely characterize $L^{p}$-$L^{q}$ boundedness of integral operators of Forelli–Rudin type acting on the Hartogs triangle $\mathbb {H}=\{(z_{1},z_{2})\in \mathbb {C}^{2}:|z_{1}| \lt |z_{2}| \lt 1\}$ for all $1\leq p,q \leq \infty $, which generalizes the characterization of $L^{p}$-$L^{q}$ 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.