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Stević, Stevo

On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball. (English) Zbl 1155.32002

Discrete Dyn. Nat. Soc. 2008, Article ID 154263, 14 p. (2008).
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.

Cited in 1 Review
Cited in 38 Documents

MSC:

32A36 Bergman spaces of functions in several complex variables
45P05 Integral operators
47G10 Integral operators
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\textit{S. Stević}, Discrete Dyn. Nat. Soc. 2008, Article ID 154263, 14 p. (2008; Zbl 1155.32002)
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