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

摘要

We introduce an integral-type operator, denoted by 13,p, on the space of holomorphic functions onthe unit ball IL c C", which is an extension of the product of composition and integral operators onthe unit disk. The operator norm of IV from the weighted Bergman space Ala' ( ) to the Bloch-typespace 13p(t) or the little Bloch-type space 131,,o(;) is calculated. The compactness of the operator ischaracterized in terms of inducing functions g and cp. Upper and lower bounds for the essentialnorm of the operatorAPa( _) 73/, ( M), when p > 1, are also given.