This HTML5 document contains 49 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
n16http://localhost/temp/predkladatel/
n19http://linked.opendata.cz/resource/domain/vavai/riv/tvurce/
n4http://linked.opendata.cz/resource/domain/vavai/projekt/
n9http://linked.opendata.cz/resource/domain/vavai/subjekt/
n8http://linked.opendata.cz/ontology/domain/vavai/
n15http://linked.opendata.cz/resource/domain/vavai/zamer/
shttp://schema.org/
skoshttp://www.w3.org/2004/02/skos/core#
n3http://linked.opendata.cz/ontology/domain/vavai/riv/
n12http://linked.opendata.cz/resource/domain/vavai/vysledek/RIV%2F68407700%3A21110%2F11%3A00189750%21RIV12-MSM-21110___/
n2http://linked.opendata.cz/resource/domain/vavai/vysledek/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
n11http://linked.opendata.cz/ontology/domain/vavai/riv/klicoveSlovo/
n13http://linked.opendata.cz/ontology/domain/vavai/riv/duvernostUdaju/
xsdhhttp://www.w3.org/2001/XMLSchema#
n18http://linked.opendata.cz/ontology/domain/vavai/riv/jazykVysledku/
n6http://linked.opendata.cz/ontology/domain/vavai/riv/aktivita/
n20http://linked.opendata.cz/ontology/domain/vavai/riv/druhVysledku/
n17http://linked.opendata.cz/ontology/domain/vavai/riv/obor/
n5http://reference.data.gov.uk/id/gregorian-year/

Statements

Subject Item
n2:RIV%2F68407700%3A21110%2F11%3A00189750%21RIV12-MSM-21110___
rdf:type
n8:Vysledek skos:Concept
dcterms:description
The Hardy averaging operator $Af(x):=\\frac1x\\int_0\\sp x f(t)\\,dt$ is known to map boundedly the `source\' space $S^p$ of functions on $(0,1)$ with finite integral $\\int_0^1 \\esup_{t\\in(x,1)}\\frac1{t}\\int_0^t |f|^p dx$ into the `target\' space $T^p$ of functions on $(0,1)$ with finite integral $\\int_0^1 \\esup_{t\\in(x,1)}|f(t)|^p dx$ whenever $1<p<\\infty$. Moreover, the spaces $S^p$ and $T^p$ are optimal within the fairly general context of all Banach lattices. We prove a~duality relation between such spaces. We in fact work with certain (more general) weighted modifications of these spaces. We prove optimality results for the action of $A$ on such spaces and point out some applications to the variable-exponent spaces. Our method of proof of the main duality result is based on certain discretization technique which leads to a~discretized characterization of the optimal spaces. The Hardy averaging operator $Af(x):=\\frac1x\\int_0\\sp x f(t)\\,dt$ is known to map boundedly the `source\' space $S^p$ of functions on $(0,1)$ with finite integral $\\int_0^1 \\esup_{t\\in(x,1)}\\frac1{t}\\int_0^t |f|^p dx$ into the `target\' space $T^p$ of functions on $(0,1)$ with finite integral $\\int_0^1 \\esup_{t\\in(x,1)}|f(t)|^p dx$ whenever $1<p<\\infty$. Moreover, the spaces $S^p$ and $T^p$ are optimal within the fairly general context of all Banach lattices. We prove a~duality relation between such spaces. We in fact work with certain (more general) weighted modifications of these spaces. We prove optimality results for the action of $A$ on such spaces and point out some applications to the variable-exponent spaces. Our method of proof of the main duality result is based on certain discretization technique which leads to a~discretized characterization of the optimal spaces.
dcterms:title
Duals of optimal spaces for the Hardy averaging operator Duals of optimal spaces for the Hardy averaging operator
skos:prefLabel
Duals of optimal spaces for the Hardy averaging operator Duals of optimal spaces for the Hardy averaging operator
skos:notation
RIV/68407700:21110/11:00189750!RIV12-MSM-21110___
n8:predkladatel
n9:orjk%3A21110
n3:aktivita
n6:P n6:Z
n3:aktivity
P(GA201/07/0388), P(GA201/08/0383), Z(MSM0021620839), Z(MSM6840770010)
n3:cisloPeriodika
4
n3:dodaniDat
n5:2012
n3:domaciTvurceVysledku
n19:9590951
n3:druhVysledku
n20:J
n3:duvernostUdaju
n13:S
n3:entitaPredkladatele
n12:predkladatel
n3:idSjednocenehoVysledku
195557
n3:idVysledku
RIV/68407700:21110/11:00189750
n3:jazykVysledku
n18:eng
n3:klicovaSlova
Hardy averaging operator, optimal target and domain spaces, associate spaces, discretization, Banach lattice, weights, weighted spaces, variable-exponent spaces
n3:klicoveSlovo
n11:optimal%20target%20and%20domain%20spaces n11:discretization n11:Hardy%20averaging%20operator n11:variable-exponent%20spaces n11:associate%20spaces n11:weighted%20spaces n11:weights n11:Banach%20lattice
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[84C8C8138208]
n3:nazevZdroje
Journal of Analysis and its Applications
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n4:GA201%2F08%2F0383 n4:GA201%2F07%2F0388
n3:rokUplatneniVysledku
n5:2011
n3:svazekPeriodika
30
n3:tvurceVysledku
Pick, L. Nekvinda, Aleš
n3:wos
000298442900004
n3:zamer
n15:MSM0021620839 n15:MSM6840770010
s:issn
0232-2064
s:numberOfPages
22
n16:organizacniJednotka
21110