Bohr radius for Banach spaces on simply connected domains

[2111.10880] Bohr radius for Banach spaces on simply connected domains Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Complex Variables arXiv:2111.10880 (math) [Submitted on 21 Nov 2021 ( v1 ), last revised 24 Nov 2021 (this version, v2)] Title: Bohr radius for Banach spaces on simply connected domains Authors: Vasudevarao Allu , Himadri Halder View a PDF of the paper titled Bohr radius for Banach spaces on simply connected domains, by Vasudevarao Allu and Himadri Halder View PDF HTML (experimental) Abstract: Let $H^{\infty}(\Omega,X)$ be the space of bounded analytic functions $f(z)=\sum_{n=0}^{\infty} x_{n}z^{n}$ from a proper simply connected domain $\Omega$ containing the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ into a complex Banach space $X$ with $\norm{f}_{H^{\infty}(\Omega,X)} \leq 1$. Let $\phi=\{\phi_{n}(r)\}_{n=0}^{\infty}$ with $\phi_{0}(r)\leq 1$ such that $\sum_{n=0}^{\infty} \phi_{n}(r)$ converges locally uniformly with respect to $r \in [0,1)$. For $1\leq p,q<\infty$, we denote \begin{equation*} R_{p,q,\phi}(f,\Omega,X)= \sup \left\{r \geq 0: \norm{x_{0}}^p \phi_{0}(r) + \left(\sum_{n=1}^{\infty} \norm{x_{n}}\phi_{n}(r)\right)^q \leq \phi_{0}(r)\right\} \end{equation*} and define the Bohr radius associated with $\phi$ by $$R_{p,q,\phi}(\Omega,X)=\inf \left\{R_{p,q,\phi}(f,\Omega,X): \norm{f}_{H^{\infty}(\Omega,X)} \leq 1\right\}.$$ In this article, we extensively study the Bohr radius $R_{p,q,\phi}(\Omega,X)$, when $X$ is an arbitrary Banach space and $X$ is certain Hilbert space. Furthermore, we establish the Bohr inequality for the operator-valued Cesáro operator and Bernardi operator. Comments: We revise the proof of Theorem 1.2. This paper contains 23 pages, 12 figures, 6 tables Subjects: Complex Variables (math.CV) ; Functional Analysis (math.FA) MSC classes: 46E40, 47A56, 47A63, 46B20, 30B10, 30C20, 30C65 Cite as: arXiv:2111.10880 [math.CV] (or arXiv:2111.10880v2 [math.CV] for this version) https://doi.org/10.48550/arXiv.2111.10880 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Proceedings of the Edinburgh Mathematical Society 67 (2024), 113-141 Related DOI : https://doi.org/10.1017/S0013091523000688 Focus to learn more DOI(s) linking to related resources Submission history From: Himadri Halder [ view email ] [v1] Sun, 21 Nov 2021 19:17:46 UTC (210 KB) [v2] Wed, 24 Nov 2021 13:41:34 UTC (211 KB) Full-text links: Access Paper: View a PDF of the paper titled Bohr radius for Banach spaces on simply connected domains, by Vasudevarao Allu and Himadri Halder View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2021-11 Change to browse by: math math.FA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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