About: Hardy averaging operator on generalized Banach function spaces and duality

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Hardy averaging operator on generalized Banach function spaces and duality Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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 maximal operator $M$ 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 Lebesgue spaces $L^{p(cdot)}(Omega)$ , as an extension of cite{NP} and cite{NP2} in the case when $n=1$ and $Omega$ is a bounded interval. 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 maximal operator $M$ 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 Lebesgue spaces $L^{p(cdot)}(Omega)$ , as an extension of cite{NP} and cite{NP2} in the case when $n=1$ and $Omega$ is a bounded interval. (en)
Title	Hardy averaging operator on generalized Banach function spaces and duality Hardy averaging operator on generalized Banach function spaces and duality (en)
skos:prefLabel	Hardy averaging operator on generalized Banach function spaces and duality Hardy averaging operator on generalized Banach function spaces and duality (en)
skos:notation	RIV/68407700:21110/13:00215577!RIV14-MSM-21110___
http://linked.open...avai/predkladatel	Fakulta stavební
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Nekvinda, Aleš
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta stavební
http://linked.open...dnocenehoVysledku	77065
http://linked.open...ai/riv/idVysledku	RIV/68407700:21110/13:00215577
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Hardy averaging operator; generalized Banach function space; optimal (en)
http://linked.open.../riv/klicoveSlovo	Hardy averaging operator optimal generalized Banach function space
http://linked.open...odStatuVydavatele	CH - Švýcarská konfederace
http://linked.open...ontrolniKodProRIV	[21E2F276BA77]
http://linked.open...i/riv/nazevZdroje	Zeitschrift für Analysis und ihre Anwendungen
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	32
http://linked.open...iv/tvurceVysledku	Nekvinda, Aleš Mizuta, Y. Shimomura, T.
http://linked.open...ain/vavai/riv/wos	000320488000007
issn	0232-2064
number of pages	23 (xsd:int)
http://localhost/t...ganizacniJednotka	21110

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software