Optimality of Function Spaces in Sobolev Embeddings

  • Luboš Pick
Part of the International Mathematical Series book series (IMAT, volume 8)


Abstract We study the optimality of function spaces that appear in Sobolev embeddings. We focus on rearrangement-invariant Banach function spaces. We apply methods of interpolation theory.

It is a great honor for me to contribute to this volume dedicated to the centenary of S.L. Sobolev, one of the greatest analysts of the XXth century. The paper concerns a topic belonging to an area bearing the name, called traditionally Sobolev inequalities or Sobolev embeddings. The focus will be on the sharpness or optimality of function spaces appearing in these embeddings. The results presented in this paper were established in recent years. Most of them were obtained in collaboration with Ron Kerman and Andrea Cianchi.


Function Space Sobolev Inequality Lebesgue Space Orlicz Space Domain Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Luboš Pick
    • 1
  1. 1.Charles UniversityPraha 8

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