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Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 154263, 14 pages
http://dx.doi.org/10.1155/2008/154263
Research Article

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

Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III, 11000 Beograd, Serbia

Received 1 May 2008; Accepted 20 July 2008

Academic Editor: Leonid Berezansky

Copyright © 2008 Stevo Stević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce an integral-type operator, denoted by π‘ƒπ‘”πœ‘, on the space of holomorphic functions on the unit ball π”ΉβŠ‚β„‚π‘›, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of π‘ƒπ‘”πœ‘ from the weighted Bergman space 𝐴𝑝𝛼(𝔹) to the Bloch-type space β„¬πœ‡(𝔹) or the little Bloch-type space β„¬πœ‡,0(𝔹) is calculated. The compactness of the operator is characterized in terms of inducing functions 𝑔 and πœ‘. Upper and lower bounds for the essential norm of the operator π‘ƒπ‘”πœ‘βˆΆπ΄π‘π›Ό(𝔹)β†’β„¬πœ‡(𝔹), when 𝑝>1, are also given.