Abstract and Applied Analysis (Jan 2009)

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

  • M. Haji Shaabani,
  • B. Khani Robati

DOI
https://doi.org/10.1155/2009/720217
Journal volume & issue
Vol. 2009

Abstract

Read online

We obtain a representation for the norm of certain compact weighted composition operator πΆπœ“,πœ‘ on the Hardy space 𝐻2, whenever πœ‘(𝑧)=π‘Žπ‘§+𝑏 and πœ“(𝑧)=π‘Žπ‘§βˆ’π‘. 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.