On holomorphic functions attaining their weighted norms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00390248" target="_blank" >RIV/68407700:21230/25:00390248 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13398-024-01681-1" target="_blank" >https://doi.org/10.1007/s13398-024-01681-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-024-01681-1" target="_blank" >10.1007/s13398-024-01681-1</a>
Alternative languages
Result language
angličtina
Original language name
On holomorphic functions attaining their weighted norms
Original language description
We study holomorphic functions attaining weighted norms and its connections with the classical theory of norm attaining holomorphic functions. We prove that there are polynomials on & ell;pdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ell _p$$end{document} which attain their weighted but not their supremum norm and viceversa. Nevertheless, we also prove that in the context of polynomials of fixed degree both norms are in fact equivalent. This leads us to the main problem of the paper, namely, whether the holomorphic functions attaining their weighted norm are dense. Although we exhibit an example where this does not hold, as the main theorem of our paper, we prove the denseness provided the domain space is uniformly convex. In fact, we provide a Bollob & aacute;s type theorem in this setting. For the proof of such a result we develop a new geometric technique.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA23-04776S" target="_blank" >GA23-04776S: Interplay of algebraic, metric, geometric and topological structures on Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
ISSN
1578-7303
e-ISSN
1579-1505
Volume of the periodical
119
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
22
Pages from-to
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UT code for WoS article
001362397300001
EID of the result in the Scopus database
2-s2.0-85209731406