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Abstract and Applied Analysis
Volume 2009, Article ID 720217, 13 pages
Research Article

On the Norm of Certain Weighted Composition Operators on the Hardy Space

Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran

Received 22 January 2009; Revised 9 March 2009; Accepted 8 May 2009

Academic Editor: Stevo Stevic

Copyright © 2009 M. Haji Shaabani and B. Khani Robati. 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.


We obtain a representation for the norm of certain compact weighted composition operator 𝐢 πœ“ , πœ‘ on the Hardy space 𝐻 2 , whenever πœ‘ ( 𝑧 ) = π‘Ž 𝑧 + 𝑏 and πœ“ ( 𝑧 ) = π‘Ž 𝑧 βˆ’ 𝑏 . We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on πœ‘ and πœ“ . Moreover, we characterize the norm and essential norm of such operators in a special case.