Entropy numbers of finite-dimensional Lorentz space embeddings

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00384873" target="_blank" >RIV/68407700:21340/25:00384873 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4064/sm240409-15-2" target="_blank" >https://doi.org/10.4064/sm240409-15-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/sm240409-15-2" target="_blank" >10.4064/sm240409-15-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Entropy numbers of finite-dimensional Lorentz space embeddings

Popis výsledku v původním jazyce

The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between finite-dimensional Lorentz spaces & ell;np,q in all regimes; our results are sharp up to constants. This generalizes classical results obtained by Sch & uuml;tt (in the case of Banach spaces) and by Edmunds and Triebel, by K & uuml;hn, as well as by Gu & eacute;don and Litvak (in the case of quasi-Banach spaces) for entropy numbers of identities between finte-dimensional Lebesgue sequence spaces & ell;np . We employ techniques such as interpolation and volume comparison as well as techniques from sparse approximation and combinatorial arguments. Further, we characterize entropy numbers of embeddings between finite-dimensional symmetric quasi-Banach spaces in terms of best s-term approximation numbers.

Název v anglickém jazyce

Entropy numbers of finite-dimensional Lorentz space embeddings

Popis výsledku anglicky

The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between finite-dimensional Lorentz spaces & ell;np,q in all regimes; our results are sharp up to constants. This generalizes classical results obtained by Sch & uuml;tt (in the case of Banach spaces) and by Edmunds and Triebel, by K & uuml;hn, as well as by Gu & eacute;don and Litvak (in the case of quasi-Banach spaces) for entropy numbers of identities between finte-dimensional Lebesgue sequence spaces & ell;np . We employ techniques such as interpolation and volume comparison as well as techniques from sparse approximation and combinatorial arguments. Further, we characterize entropy numbers of embeddings between finite-dimensional symmetric quasi-Banach spaces in terms of best s-term approximation numbers.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-04720S" target="_blank" >GA23-04720S: Jemné vlastnosti funkcí, operátorů a prostorů funkcí</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

Studia Mathematica

ISSN

0039-3223

e-ISSN

1730-6337

Svazek periodika

283

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

27

Strana od-do

105-131

Kód UT WoS článku

001506916600001

EID výsledku v databázi Scopus

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