A note on one-sided maximal operator in $L^{p(.)}(mathbb{R})$

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F10%3A00178871" target="_blank" >RIV/68407700:21110/10:00178871 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A note on one-sided maximal operator in $L^{p(.)}(mathbb{R})$
Original language description
Consider one-sided Hardy-Littlewood maximal operator on the general Lebesgue space with variable exponent. It is known a local sufficient condition to the function $p(.)$ for the boundedness of the one-sided maximal operator on $L^{p(.)}(\mathbb{R})$ provided $p(.)$ is a constant function in a neighborhood of infinity. Our main aim is to find a weaker condition to $p(.)$ at infinity to guarantee the boundedness of the one-sided maximal operator on $L^{p(.)}(\mathbb{R})$. We will show two different sufficient conditions to the behavior of $p(.)$ at infinity under which the one-sided maximal operator is bounded on $L^{p(.)}(\mathbb{R})$.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F08%2F0383" target="_blank" >GA201/08/0383: Function Spaces, Weighted Inequalities and Interpolation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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