Maximal operator on variable Lebesgue spaces with radial exponent

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F19%3A00337976" target="_blank" >RIV/68407700:21110/19:00337976 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jmaa.2019.04.056" target="_blank" >https://doi.org/10.1016/j.jmaa.2019.04.056</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2019.04.056" target="_blank" >10.1016/j.jmaa.2019.04.056</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Maximal operator on variable Lebesgue spaces with radial exponent

Popis výsledku v původním jazyce

Consider general Lebesgue spaces with variable exponent $p(.)$ and the Hardy-Littlewood maximal operator $M$. There are known sufficient conditions for $p(.)$ which guarantee the boundedness of $M$ on these spaces. These conditions are divided into two categories. The first one controls a local behavior of $p(.)$ and the second one gives sufficient conditions to $p(.)$ at infinity. We put in this paper emphasis to properties of $p(.)$ at infinity. Certain sufficient conditions to $p(.)$ at infinity are known to guarantee the boundedness of the maximal operator on variable Lebesgue spaces. In this paper we find a weaker condition to $p(.)$ which still preserves the boundedness of $M$. Moreover, it is known that there exist some functions $p(.)$ which have no limit at infinity for which the maximal operator is bounded. We give here a wider class of such functions $p(.)$ with no limit which nevertheless preserves the boundedness of $M$.

Název v anglickém jazyce

Maximal operator on variable Lebesgue spaces with radial exponent

Popis výsledku anglicky

Consider general Lebesgue spaces with variable exponent $p(.)$ and the Hardy-Littlewood maximal operator $M$. There are known sufficient conditions for $p(.)$ which guarantee the boundedness of $M$ on these spaces. These conditions are divided into two categories. The first one controls a local behavior of $p(.)$ and the second one gives sufficient conditions to $p(.)$ at infinity. We put in this paper emphasis to properties of $p(.)$ at infinity. Certain sufficient conditions to $p(.)$ at infinity are known to guarantee the boundedness of the maximal operator on variable Lebesgue spaces. In this paper we find a weaker condition to $p(.)$ which still preserves the boundedness of $M$. Moreover, it is known that there exist some functions $p(.)$ which have no limit at infinity for which the maximal operator is bounded. We give here a wider class of such functions $p(.)$ with no limit which nevertheless preserves the boundedness of $M$.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00580S" target="_blank" >GA18-00580S: Prostory funkcí a aproximace</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Its Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

477

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

961-986

Kód UT WoS článku

000470802500004

EID výsledku v databázi Scopus

2-s2.0-85065825259