About: Duals of optimal spaces for the Hardy averaging operator

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

About: Duals of optimal spaces for the Hardy averaging operator 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	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. (en)
Title	Duals of optimal spaces for the Hardy averaging operator Duals of optimal spaces for the Hardy averaging operator (en)
skos:prefLabel	Duals of optimal spaces for the Hardy averaging operator Duals of optimal spaces for the Hardy averaging operator (en)
skos:notation	RIV/68407700:21110/11:00189750!RIV12-MSM-21110___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/07/0388), P(GA201/08/0383), Z(MSM0021620839), Z(MSM6840770010)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2012
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	195557
http://linked.open...ai/riv/idVysledku	RIV/68407700:21110/11:00189750
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Hardy averaging operator, optimal target and domain spaces, associate spaces, discretization, Banach lattice, weights, weighted spaces, variable-exponent spaces (en)
http://linked.open.../riv/klicoveSlovo	weights Banach lattice Hardy averaging operator associate spaces discretization optimal target and domain spaces variable-exponent spaces weighted spaces
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[84C8C8138208]
http://linked.open...i/riv/nazevZdroje	Journal of Analysis and its Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Function Spaces, Weighted Inequalities and Interpolation Modern methods in potential theory and function spaces
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	30
http://linked.open...iv/tvurceVysledku	Nekvinda, Aleš Pick, L.
http://linked.open...ain/vavai/riv/wos	000298442900004
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace Aplikovaná matematika v technických a fyzikálních vědách
issn	0232-2064
number of pages	22 (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, 38 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software