INSTYTUT MATEMATYCZNY · POLSKA AKADEMIA NAUK STUDIA MATHEMATICA ISSN: 0039-3223(p) 1730-6337(e)

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Sobolev-type spaces from generalized Poincaré inequalities

Toni Heikkinen¹, Pekka Koskela², Heli Tuominen³
Studia Math. 181 (2007), 1-16
doi:10.4064/sm181-1-1

Abstract: We define a Sobolev space by means of a generalized Poincaré inequality and relate it to a corresponding space based on upper gradients.


MSC (2000): Primary 46E35; Secondary 46E30, 26D10.
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1. Department of Mathematics and Statistics
   P.O. Box 35
   FI-40014 University of Jyväskylä, Finland
   
2. Department of Mathematics and Statistics
   P.O. Box 35
   FI-40014 University of Jyväskylä, Finland
   
3. Department of Mathematics and Statistics
   P.O. Box 35
   FI-40014 University of Jyväskylä, Finland
   

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