The Forelli-Rudin type theorem and a class of integral operator related to hypergeometric function

The boundedness and the accurate norm of a class of integral operator related to hypergeometric function are discussed by using the theory of hypergeometric function and Schurs test. The establishment of the main results not only builds the bridge between holomorphic Forelli-Rudin type theorem and harmonic Forelli-Rudin type theorem, but also deepens the understanding of the Bergman projection and Berezin transform.