Abstract and Applied Analysis
Volume 2009 (2009), Article ID 720217, 13 pages
doi:10.1155/2009/720217
On the norm of certain weighted composition operators on the Hardy space
M.Haji Shaabani
and B. Khani Robati
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran
Abstract
We obtain a representation for the norm of certain compact weighted composition operator Cψ,φ on the Hardy space H2, whenever φ(z)=az+b and ψ(z)=az−b. We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on φ and ψ. Moreover, we characterize the norm and essential norm of such operators in a special case.