On the embedding between the variable Lebesgue space Lp(⋅)(Ω) and the Orlicz space L(log⁡L)α(Ω)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00602336" target="_blank" >RIV/67985840:_____/25:00602336 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2024.129081" target="_blank" >https://doi.org/10.1016/j.jmaa.2024.129081</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2024.129081" target="_blank" >10.1016/j.jmaa.2024.129081</a>

Result language
angličtina
Original language name
On the embedding between the variable Lebesgue space Lp(⋅)(Ω) and the Orlicz space L(log⁡L)α(Ω)
Original language description
We give a sharp sufficient condition on the distribution function, |{x∈Ω: p(x)≤1+λ}|, λ>0, of the exponent function p(⋅):Ω→[1,∞) that implies the embedding of the variable Lebesgue space L^{p(⋅)}(Ω) into the Orlicz space L(log⁡L)^{α}(Ω), α>0, where Ω is an open set with finite Lebesgue measure. As applications of our results, we first give conditions that imply the strong differentiation of integrals of functions in L^{p(⋅)}((0,1)^n), n>1. We then consider the integrability of the maximal function on variable Lebesgue spaces, where the exponent function p(⋅) approaches 1 in value on some part of the domain.
Czech name
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Czech description
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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

Project
<a href="/en/project/GA23-04720S" target="_blank" >GA23-04720S: Fine properties of functions, operators and function spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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