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On Whitney-type Characterization of Approximate Differentiability on Metric Measure Spaces

Published online by Cambridge University Press:  20 November 2018

E. Durand-Cartagena
Affiliation:
Departamento de Matemática Aplicada, ETSI Industriales, UNED c/Juan del Rosal 12 Ciudad Universitaria, 28040 Madrid, Spain. e-mail: edurand@ind.uned.es
L. Ihnatsyeva
Affiliation:
Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki, Finland. e-mail: lizaveta.ihnatsyeva@helsinki.fi, riikka.korte@helsinki.fi
R. Korte
Affiliation:
Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki, Finland. e-mail: lizaveta.ihnatsyeva@helsinki.fi, riikka.korte@helsinki.fi
M. Szumańska
Affiliation:
Faculty of Mathematics, Informatics, and Mechanics University of Warsaw, Banacha 2, 02-097 Warszawa, Poland. e-mail: m.szumanska@mimuw.edu.pl
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Abstract

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We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, $BV$, and maximal functions.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

The first author was partially supported by grant MTM2009-07848 (Spain). The second, the third and the fourth authors were supported by the Academy of Finland (grants 252293, 250403 and 138738). The fourth author was partially supported by MNiSW Grant no N N201 397737, Nonlinear partial differential equations: geometric and variational problems.

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