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  • Research Article
  • Open Access

Hölder Quasicontinuity in Variable Exponent Sobolev Spaces

Journal of Inequalities and Applications20072007:032324

  • Received: 28 May 2006
  • Accepted: 25 December 2006
  • Published:


We show that a function in the variable exponent Sobolev spaces coincides with a Hölder continuous Sobolev function outside a small exceptional set. This gives us a method to approximate a Sobolev function with Hölder continuous functions in the Sobolev norm. Our argument is based on a Whitney-type extension and maximal function estimates. The size of the exceptional set is estimated in terms of Lebesgue measure and a capacity. In these estimates, we use the fractional maximal function as a test function for the capacity.


  • Continuous Function
  • Sobolev Space
  • Lebesgue Measure
  • Function Estimate
  • Maximal Function


Authors’ Affiliations

Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, Gustaf Hällströmin Katu 2b, Helsinki, 00014, Finland
Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, Oulu, 90014, Finland


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© Petteri Harjulehto et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.