Weighted composition operators on Bers-type spaces of Loo-Keng Hua domains

摘要

Let HE I , HE II , HE III and HE IV be the first, second, thirdand fourth type Loo-Keng Hua domain respectively, ? a holomorphicself-map of HE I , HE II , HE III , or HE IV and u ∈ H(M) the space ofall holomorphic functions on M ∈ {HE I ,HE II ,HE III ,HE IV }. In thispaper, motivated by the well known Hua’s matrix inequality, first someinequalities for the points in the Bers-type spaces of the Loo-Keng Huadomains are obtained, and then the boundedness and compactness of theweighted composition operators W ?,u : f 7→ u·f ?? on Bers-type spacesof these domains are characterized.