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Sharp conditions for the compactness of the Sobolev embedding on Musielak–Orlicz spaces

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  • Jan Lang
  • Osvaldo Méndez

Abstract

We prove the compactness of the Sobolev embedding for Musielak–Orlicz spaces by way of simple conditions on the Matuszewska index of the underlying space. We provide counterexamples to show the sharpness of our conditions.

Suggested Citation

  • Jan Lang & Osvaldo Méndez, 2019. "Sharp conditions for the compactness of the Sobolev embedding on Musielak–Orlicz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 292(2), pages 377-388, February.
  • Handle: RePEc:bla:mathna:v:292:y:2019:i:2:p:377-388
    DOI: 10.1002/mana.201700462
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