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The Stepanov differentiability theorem in metric measure spaces

Balogh, Zoltán ; Rogovin, Kevin ; Zürcher, Thomas

In: The Journal of Geometric Analysis, 2004, vol. 14, no. 3, p. 405-422

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    Title
    • The Stepanov differentiability theorem in metric measure spaces
    Author
    • Balogh, Zoltán. Department of Mathematics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
    • Rogovin, Kevin. Department of Mathematics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
    • Zürcher, Thomas. Department of Mathematics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • The Journal of Geometric Analysis, 2004, vol. 14, no. 3, p. 405-422. Springer-Verlag
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:315166
    Summary
    We extend Cheeger's theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov's condition. As a consequence, we obtain the analogue of Calderon's differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequality