Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 154263, 14 pages
doi: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 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.