$L^p-L^q$ boundedness of Forelli-Rudin type operators on the unit ball of ${\mathbb{C}}^n$

We completely characterize $L^p-L^q$ boundedness of two classes of Forelli-Rudin type operators on the unit ball of ${\mathbb{C}}^n$ for all $(p,q)\in [1,\mathrm{\infty }]\times [1,\mathrm{\infty }]$. The results are not only a complement to some previous results on Forelli-Rudin type operators by Kures and Zhu in 2006 and the first author in 2015, but also a high dimension extension of some results by Cheng, Fang, Wang and Yu in 2017.