On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball (Q949027)

Summary: We introduce an integral-type operator, denoted by \(P_\varphi^g\), on the space of holomorphic functions on the unit ball \(\mathbb BS\subset \mathbb C^n\), which is an extension of the product of composition and integral operators on the unit disk. The operator norm of \(P_\varphi^g\) from the weighted Bergman space \(A_\alpha^p(\mathbb B)\) to the Bloch-type space \({\mathcal B}_\mu(\mathbb B)\) or the little Bloch-type space \({\mathcal B}_{\mu,0}(\mathbb B)\) is calculated. The compactness of the operator is characterized in terms of inducing functions \(g\) and \(\varphi\). Upper and lower bounds for the essential norm of the operator \(P_\varphi^g:A_\alpha^p(\mathbb B)\to {\mathcal B}_\mu(\mathbb B)\), when \(p>1\), are also given.