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On functions with derivatives in a Lorentz space |
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| Authors: | Janne Kauhanen Pekka Koskela Jan Malý |
| Institution: | University of Jyv?skyl?, Department of Mathematics, P.O. Box 35,?FIN-40351 Jyv?skyl?, Finland. E-mail: jpkau@math.jyu.fi, FI University of Jyv?skyl?, Department of Mathematics, P.O. Box 35,?FIN-40351 Jyv?skyl?, Finland. E-mail: pkoskela@math.jyu.fi, FI 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 |
| 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. Received: 6 January 1999 / Revised version: 5 May 1999 |
| Keywords: | Mathematics Subject Classification (1991):26B10 26B35 46E35 73C50 |
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