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On functions with derivatives in a Lorentz space

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Abstract:

We establish a sharp integrability condition on the partial derivatives of a Sobolev mapping to guarantee that sets of measure zero get mapped to sets of measure zero. This condition is sharp also for continuity and differentiability almost everywhere.

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Authors and Affiliations

  1. University of Jyväskylä, Department of Mathematics, P.O. Box 35,¶FIN-40351 Jyväskylä, Finland. E-mail: jpkau@math.jyu.fi, , , , , , FI

    Janne Kauhanen

  2. University of Jyväskylä, Department of Mathematics, P.O. Box 35,¶FIN-40351 Jyväskylä, Finland. E-mail: pkoskela@math.jyu.fi, , , , , , FI

    Pekka Koskela

  3. Charles University, Department KMA of the Faculty of Mathematics and Physics, Sokolovská 83, CZ-18675 Praha 8, Czech Republic. E-mail: maly@karlin.mff.cuni.cz, , , , , , CZ

    Jan Malý

Authors
  1. Janne Kauhanen
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  2. Pekka Koskela
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  3. Jan Malý
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Received: 6 January 1999 / Revised version: 5 May 1999

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Kauhanen, J., Koskela, P. & Malý, J. On functions with derivatives in a Lorentz space. manuscripta math. 100, 87–101 (1999). https://doi.org/10.1007/s002290050197

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  • DOI: https://doi.org/10.1007/s002290050197

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