Optimality problems in Orlicz spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475499" target="_blank" >RIV/00216208:11320/23:10475499 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14330/23:00133451

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KPoXo77ASj" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KPoXo77ASj</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2023.109273" target="_blank" >10.1016/j.aim.2023.109273</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimality problems in Orlicz spaces

Popis výsledku v původním jazyce

In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the mutual relationship between the data and solution quality. The optimality of the obtained results deserves aspecial focus. It requires acareful choice of families of function spaces balancing between their expressivity, i.e. the ability to capture fine properties of the model, and their accessibility, i.e. its technical difficulty for practical use. This paper presents aunified and general approach to optimality problems in Orlicz spaces. Orlicz spaces are parametrized by a single convex function and neatly balance the expressivity and accessibility. We prove a general principle that yields an easily verifiable necessary and sufficient condition for the existence or the non-existence of an optimal Orlicz space in various tasks. We demonstrate its use in specific problems, including the continuity of Sobolev embeddings and boundedness of integral operators such as the Hardy-Littlewood maximal operator and the Laplace transform.

Název v anglickém jazyce

Optimality problems in Orlicz spaces

Popis výsledku anglicky

In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the mutual relationship between the data and solution quality. The optimality of the obtained results deserves aspecial focus. It requires acareful choice of families of function spaces balancing between their expressivity, i.e. the ability to capture fine properties of the model, and their accessibility, i.e. its technical difficulty for practical use. This paper presents aunified and general approach to optimality problems in Orlicz spaces. Orlicz spaces are parametrized by a single convex function and neatly balance the expressivity and accessibility. We prove a general principle that yields an easily verifiable necessary and sufficient condition for the existence or the non-existence of an optimal Orlicz space in various tasks. We demonstrate its use in specific problems, including the continuity of Sobolev embeddings and boundedness of integral operators such as the Hardy-Littlewood maximal operator and the Laplace transform.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF18_053%2F0016952" target="_blank" >EF18_053/0016952: Postdoc2MUNI</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Advances in Mathematics

ISSN

0001-8708

e-ISSN

1090-2082

Svazek periodika

2023

Číslo periodika v rámci svazku

432

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

58

Strana od-do

1-58

Kód UT WoS článku

001078404400001

EID výsledku v databázi Scopus

2-s2.0-85171149845