A note on the Königs domain of compact composition operators on the Bloch space

Article


Jones, M. 2011. A note on the Königs domain of compact composition operators on the Bloch space. Journal of Inequalities and Applications. https://doi.org/10.1186/1029-242X-2011-31
TypeArticle
TitleA note on the Königs domain of compact composition operators on the Bloch space
AuthorsJones, M.
Abstract

Let D be the unit disk in the complex plane. We define B0 to be the little Bloch space of functions f analytic in D which satisfy lim┬(|z|→1)⁡〖(1- |z|^2 )|f^' (z) |=0.〗 If φ:D→D is analytic then the composition operator C_φ:f→f∘φ is a continuous operator that maps B0 into itself. In this paper, we show that the compactness of C_φ, as and operator on B0, can be modelled geometrically by its principle eigenfunction. In particular, under certain necessary conditions, we relate the compactness of C_φto the geometry of Ω=σ(D) where σ satisfies Schroder’s functional equation σ∘φ=φ^' (0)σ.

PublisherSpringer
JournalJournal of Inequalities and Applications
ISSN1029-242X
Publication process dates
Deposited26 Sep 2011
Output statusPublished
Digital Object Identifier (DOI)https://doi.org/10.1186/1029-242X-2011-31
LanguageEnglish
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