On holomorphic functions attaining their weighted norms

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On holomorphic functions attaining their weighted norms

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On holomorphic functions attaining their weighted norms

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-04776S" target="_blank" >GA23-04776S: Interakce algebraických, metrických, geometrických a topologických struktur na Banachových prostorech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

ISSN

1578-7303

e-ISSN

1579-1505

Svazek periodika

119

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

22

Strana od-do

—

Kód UT WoS článku

001362397300001

EID výsledku v databázi Scopus

2-s2.0-85209731406