On a New Integral-Type Operator from the Weighted Bergman Space tothe Bloch-Type Space on the Unit Ball

摘要

We introduce an integral-type operator, denoted byPφg,on the space of holomorphic functions on the unit ballB⊂ℂn, which is an extension of the product of composition andintegral operators on the unit disk. The operator norm ofPφgfrom the weighted Bergman spaceAαp(B)to theBloch-type spaceℬμ(B)or the little Bloch-typespaceℬμ,0(B)is calculated. The compactnessof the operator is characterized in terms of inducing functionsgandφ. Upper and lower bounds for the essential normof the operatorPφg:Aαp(B)→ℬμ(B),whenp>1, are also given.