Abstract and Applied Analysis
Volume 2011 (2011), Article ID 989625, 10 pages
http://dx.doi.org/10.1155/2011/989625
Research Article

Weighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane

Stevo Stević,1 Ajay K. Sharma,2 and S. D. Sharma3

1Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia
2School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, J & K Katra 182320, India
3Department of Mathematics, University of Jammu, Jammu 180006, India

Received 25 January 2011; Accepted 3 May 2011

Academic Editor: Narcisa C. Apreutesei

Copyright © 2011 Stevo Stević et al. 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

Let 𝜓 be a holomorphic mapping on the upper half-plane Π + = { 𝑧 ∈ ℂ ∶ 𝔍 𝑧 > 0 } and 𝜑 be a holomorphic self-map of Π + . We characterize bounded weighted composition operators acting from the weighted Bergman space to the weighted-type space on the upper half-plane. Under a mild condition on 𝜓 , we also characterize the compactness of these operators.