Year: 2023
Type: preprint
Abstract: The known duality of the space of Bloch complex-valued functions on the open complex unit disc $\mathbb{D}$ is addressed under a new approach with the introduction of the concepts of Bloch molecules and Bloch-free Banach space of $\mathbb{D}$. We introduce the notion of compact Bloch mapping from $\mathbb{D}$ to a complex Banach space and establish its main properties: invariance by Möbius transformations, linearization from the Bloch-free Banach space of $\mathbb{D}$, 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.
Source: arXiv (Cornell University)
Authors: Jiménez-Vargas, A., Ruiz-Casternado, D.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4385645309