Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces. (16th May 2012)

• Record Type: Journal Article
• Authors: Colonna, Flavia; Li, Songxiao
• Other Names: Zhao Ruhan Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2012(2012)
• Publication Date: 2012-05-16
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2012/454820
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : The logarithmic Bloch spaceℬ log is the Banach space of analytic functions on the open unit disk𝔻 whose elementsf satisfy the condition∥ f ∥ = sup z ∈ 𝔻 ( 1 - | z | 2 ) log (2 / ( 1 - | z | 2 )) | f ′ ( z ) | < ∞ . In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceH p (with1 ≤ p ≤ ∞ ) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingH p into the little logarithmic Bloch space defined as the subspace ofℬ log consisting of the functionsf such thatlim | z | → 1 ( 1 - | z | 2 ) log (2 / ( 1 - | z | 2 )) | f ′ ( z ) | = 0 .