Hardy averaging operator on generalized Banach function spaces and duality

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F13%3A00215577" target="_blank" >RIV/68407700:21110/13:00215577 - 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
Hardy averaging operator on generalized Banach function spaces and duality
Original language description
Let $Af(x):=frac{1}{|B(0,|x|)|} int_{B(0,|x|)} f(t) dt$ be the $n$-dimensional Hardy averaging operator. It is well known that $A$ is bounded on $Lsp p(Omega)$ with an open set $Omega subset mathbb{R}^n$ whenever $1<pleqinfty$. We improve this result within the framework of generalized Banach function spaces. We in fact find the `source' space $S_X$, which is strictly larger than $X$, and the `target' space $T_X$, which is strictly smaller than $X$, under the assumption that the Hardy-Littlewood maximaloperator $M$ is bounded from $X$ into $X$, and prove that $A$ is bounded from $S_X$ into $T_X$. We prove optimality results for the action of $A$ and its associate operator $A'$ on such spaces and present applications of our results to variable Lebesguespaces $L^{p(cdot)}(Omega)$ , as an extension of cite{NP} and cite{NP2} in the case when $n=1$ and $Omega$ is a bounded interval.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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