## Abstract and Applied Analysis

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

#### Abstract

We obtain a representation for the norm of certain compact weighted composition operator ${C}_{\psi ,\varphi }$ on the Hardy space ${H}^{2}$, whenever $\varphi (z)=az+b$ and $\psi (z)=az-b$. We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on $\varphi$ and $\psi$. Moreover, we characterize the norm and essential norm of such operators in a special case.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 720217, 13 pages.

Dates
First available in Project Euclid: 16 March 2010

https://projecteuclid.org/euclid.aaa/1268745584

Digital Object Identifier
doi:10.1155/2009/720217

Mathematical Reviews number (MathSciNet)
MR2533571

Zentralblatt MATH identifier
1176.47023

#### Citation

Haji Shaabani, M.; Khani Robati, B. On the Norm of Certain Weighted Composition Operators on the Hardy Space. Abstr. Appl. Anal. 2009 (2009), Article ID 720217, 13 pages. doi:10.1155/2009/720217. https://projecteuclid.org/euclid.aaa/1268745584

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