Compact Bloch mappings on the complex unit disc

2023/08/04 by A. Jiménez-Vargas, Jiménez-Vargas, A., D. Ruiz-Casternado +1
Mathematics · #30H30 #46E15 #46E40 #47B38 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2308.02461

openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The known duality of the space of Bloch complex-valued functions on the open complex unit disc \mathbbD is addressed under a new approach with the introduction of the concepts of Bloch molecules and Bloch-free Banach space of \mathbbD. We introduce the notion of compact Bloch mapping from \mathbbD to a complex Banach space and establish its main properties: invariance by Möbius transformations, linearization from the Bloch-free Banach space of \mathbbD, factorization of their derivatives, inclusion properties, Banach ideal property and transposition on the Bloch function space. We state Bloch versions of the classical theorems of Schauder, Gantmacher and Davis-Figiel-Johnson-Pelczyński.

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