Maximal operator on variable Lebesgue spaces for almost monotone radial exponent

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Maximal operator on variable Lebesgue spaces for almost monotone radial exponent

Original language description

Consider general Lebesgue spaces with variable exponent $p$. There are known classes $\\mathcal{L}$ and $\\mathcal{N}$ of functions $p$ such that the Hardy-Littlewood maximal operator is bounded on these spaces provided $p\\in\\mathcal{L}\\cap\\mathcal{P}$. The class $\\mathcal{L}$ controls a local properties of $p$ and $\\mathcal{N}$ gives a behavior of $p$ at infinity. We lay in this paper emphasis to properties of $p$ at infinity. We extend the class $\\mathcal{N}$ to a collection $\\mathcal{D}$ of functions $p$ such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue spaces provided $p\\in\\mathcal{L}\\cap\\mathcal{D}$ and the class $\\mathcal{D}$ is essentially greater than $\\mathcal{N}$.Moreover, it is practically very easy to verify the condition $p\\in\\mathcal{D}$.

Czech name

Maximální operátor na Lebesgueových prostorech pro skoro radiální monotónní exponent

Czech description

Consider general Lebesgue spaces with variable exponent $p$. There are known classes $\\mathcal{L}$ and $\\mathcal{N}$ of functions $p$ such that the Hardy-Littlewood maximal operator is bounded on these spaces provided $p\\in\\mathcal{L}\\cap\\mathcal{P}$. The class $\\mathcal{L}$ controls a local properties of $p$ and $\\mathcal{N}$ gives a behavior of $p$ at infinity. We lay in this paper emphasis to properties of $p$ at infinity. We extend the class $\\mathcal{N}$ to a collection $\\mathcal{D}$ of functions $p$ such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue spaces provided $p\\in\\mathcal{L}\\cap\\mathcal{D}$ and the class $\\mathcal{D}$ is essentially greater than $\\mathcal{N}$.Moreover, it is practically very easy to verify the condition $p\\in\\mathcal{D}$.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2008

Confidentiality

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

Name of the periodical

Journal of Mathematical Analysis and Its Applications

ISSN

0022-247X

e-ISSN

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Volume of the periodical

338

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

20

Pages from-to

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UT code for WoS article

000253172000053

EID of the result in the Scopus database

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