Attributes | Values |
---|
rdf:type
| |
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
| |
http://linked.open...avai/riv/aktivity
| - P(GA201/07/0388), P(GA201/08/0383), Z(MSM0021620839), Z(MSM6840770010)
|
http://linked.open...iv/cisloPeriodika
| |
http://linked.open...vai/riv/dodaniDat
| |
http://linked.open...aciTvurceVysledku
| |
http://linked.open.../riv/druhVysledku
| |
http://linked.open...iv/duvernostUdaju
| |
http://linked.open...titaPredkladatele
| |
http://linked.open...dnocenehoVysledku
| |
http://linked.open...ai/riv/idVysledku
| - RIV/68407700:21110/11:00189750
|
http://linked.open...riv/jazykVysledku
| |
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
| |
http://linked.open...odStatuVydavatele
| - DE - Spolková republika Německo
|
http://linked.open...ontrolniKodProRIV
| |
http://linked.open...i/riv/nazevZdroje
| - Journal of Analysis and its Applications
|
http://linked.open...in/vavai/riv/obor
| |
http://linked.open...ichTvurcuVysledku
| |
http://linked.open...cetTvurcuVysledku
| |
http://linked.open...vavai/riv/projekt
| |
http://linked.open...UplatneniVysledku
| |
http://linked.open...v/svazekPeriodika
| |
http://linked.open...iv/tvurceVysledku
| |
http://linked.open...ain/vavai/riv/wos
| |
http://linked.open...n/vavai/riv/zamer
| |
issn
| |
number of pages
| |
http://localhost/t...ganizacniJednotka
| |