Notes on absolutely continuous functions of several variables

Abstract

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.

Keywords

• Notes
• absolutely
• continuous
• functions
• several
• variables