Compact composition operators on Besov spaces

2003/07/08 by Maria Tjani · 4 citations
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Advanced Banach Space Theory

paper · pdf · doi:10.1090/s0002-9947-03-03354-3

Abstract

We give a Carleson measure characterization of the compact composition operators on Besov spaces. We use this characterization to show that every compact composition operator on a Besov space is compact on the Bloch space. Finally we give conditions that guarantee that the converse holds.

Citations

• The Essential Norm of a Composition Operator

Cited by

• Weighted composition operators on weighted Fock spaces
• Slice regular Besov spaces of hyperholomorphic functions and composition operators
• Rhaly operators acting on Hardy, Bergman, and Dirichlet spaces
• Cesàro-type operators acting on Dirichlet spaces

Related

• Compact composition operators on BMOA and the Bloch space
• Differences of composition operators from analytic Besov spaces into little Bloch type spaces
• Compact Composition Operators on the Bloch Space in Bounded Symmetric Domains
• Composition operators on the spaces of Harmonic Bloch functions
• Vanishing Carleson measures and power compact weighted composition operators