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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F05%3A00001313%21RIV06-MSM-11320___
rdf:type
skos:Concept n16:Vysledek
dcterms:description
Let $\Omega\subset\rn$ be a domain. The result of J. Kauhanen, P. Koskela and J. Mal\'y \cite{KKM} states that a function $f:\Omega\to\er$ with a derivative in the Lorentz space $ L^{n,1}(\Omega,\rn)$ is $n$-absolutely continuous in the sense of \cite{M}. We give an example of an absolutely continuous function of two variables, whose derivative is not in $L^{2,1}$. The boundary behaviour of $n$-absolutely continuous functions is also studied. Je zkonstruován příklad absolutně spojité funkce dvou proměnných, která neleží v Lorentzově prostoru $L^{2,1}$. Je také studováno hraniční chování $n$-absolutně spojitých funkcí. Let $\Omega\subset\rn$ be a domain. The result of J. Kauhanen, P. Koskela and J. Mal\'y \cite{KKM} states that a function $f:\Omega\to\er$ with a derivative in the Lorentz space $ L^{n,1}(\Omega,\rn)$ is $n$-absolutely continuous in the sense of \cite{M}. We give an example of an absolutely continuous function of two variables, whose derivative is not in $L^{2,1}$. The boundary behaviour of $n$-absolutely continuous functions is also studied.
dcterms:title
Notes on absolutely continuous functions of several variables Poznámky k absolutně spojitým funkcím více proměnných Notes on absolutely continuous functions of several variables
skos:prefLabel
Poznámky k absolutně spojitým funkcím více proměnných Notes on absolutely continuous functions of several variables Notes on absolutely continuous functions of several variables
skos:notation
RIV/00216208:11320/05:00001313!RIV06-MSM-11320___
n4:strany
59;74
n4:aktivita
n15:Z
n4:aktivity
Z(MSM 113200007)
n4:cisloPeriodika
1
n4:dodaniDat
n10:2006
n4:domaciTvurceVysledku
n13:8100624
n4:druhVysledku
n17:J
n4:duvernostUdaju
n14:S
n4:entitaPredkladatele
n18:predkladatel
n4:idSjednocenehoVysledku
533111
n4:idVysledku
RIV/00216208:11320/05:00001313
n4:jazykVysledku
n11:eng
n4:klicovaSlova
Notes; absolutely; continuous; functions; several; variables
n4:klicoveSlovo
n5:Notes n5:several n5:continuous n5:variables n5:absolutely n5:functions
n4:kodStatuVydavatele
US - Spojené státy americké
n4:kontrolniKodProRIV
[02B7FAA8ADCF]
n4:nazevZdroje
Real Analysis Exchange
n4:obor
n12:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:rokUplatneniVysledku
n10:2005
n4:svazekPeriodika
30
n4:tvurceVysledku
Hencl, Stanislav
n4:zamer
n8:MSM%20113200007
s:issn
0147-1937
s:numberOfPages
16
n7:organizacniJednotka
11320