Maximal operator on variable Lebesgue spaces with radial exponent
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Maximal operator on variable Lebesgue spaces with radial exponent
Original language description
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 $M$.
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/GA18-00580S" target="_blank" >GA18-00580S: Function Spaces and Approximation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Its Applications
ISSN
0022-247X
e-ISSN
1096-0813
Volume of the periodical
477
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
961-986
UT code for WoS article
000470802500004
EID of the result in the Scopus database
2-s2.0-85065825259