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.