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

Abstract

We introduce an integral-type operator, denoted by Pφg, on the space of holomorphic functions on the unit ball B⊂ℂn, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of Pφg from the weighted Bergman space Aαp(B) to the Bloch-type space ℬμ(B) or the little Bloch-type space ℬμ,0(B) is calculated. The compactness of the operator is characterized in terms of inducing functions g and φ. Upper and lower bounds for the essential norm of the operator Pφg:Aαp(B)→ℬμ(B), when p>1, are also given.