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  • 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.
  • 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. (en)
  • 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. (cs)
Title
  • Notes on absolutely continuous functions of several variables
  • Notes on absolutely continuous functions of several variables (en)
  • Poznámky k absolutně spojitým funkcím více proměnných (cs)
skos:prefLabel
  • Notes on absolutely continuous functions of several variables
  • Notes on absolutely continuous functions of several variables (en)
  • Poznámky k absolutně spojitým funkcím více proměnných (cs)
skos:notation
  • RIV/00216208:11320/05:00001313!RIV06-MSM-11320___
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  • RIV/00216208:11320/05:00001313
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  • Notes; absolutely; continuous; functions; several; variables (en)
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  • 30
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  • Hencl, Stanislav
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  • 0147-1937
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  • 11320
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