  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 $(p,
q)\in [1, \infty]\times [1, \infty]$. 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.
