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Shaabani, M. Haji; Khani Robati, B.

On the norm of certain weighted composition operators on the Hardy space. (English) Zbl 1176.47023

Abstr. Appl. Anal. 2009, Article ID 720217, 13 p. (2009).
Summary: 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.

Cited in 7 Documents

MSC:

47B33 Linear composition operators
46E15 Banach spaces of continuous, differentiable or analytic functions
30H10 Hardy spaces
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References:

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