Absolutely continuous functions in R n

For each 0 < α < 1 we consider a natural n-dimensional extension of the classical notion of absolute continuous function. We compare it with the Malý's and Hencl's definitions. It follows that each α-absolute continuous function is continuous, weak differentiable with gradient in L n...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2005-03, Vol.303 (1), p.119-134
Main Author: Bongiorno, Donatella
Format: Article
Language:English
Subjects:
Absolutely continuous functions
Sobolev spaces
α-regular intervals
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Summary:For each 0 < α < 1 we consider a natural n-dimensional extension of the classical notion of absolute continuous function. We compare it with the Malý's and Hencl's definitions. It follows that each α-absolute continuous function is continuous, weak differentiable with gradient in L n , differentiable almost everywhere and satisfies the formula on change of variables.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.08.002