Annali di Matematica Pura ed Applicata

, Volume 115, Issue 1, pp 271–294 | Cite as

Embeddings of Sobolev spaces on unbounded domains

  • J. A. S. Martins


Piecewise polynomial and Fourier approximation of functions in the Sobolev spaces Open image in new window on unbounded domains Θ ⊂ Rn are applied to the study of the type of compact embeddings into appropriate Lebesgue and Orlicz spaces. It is shown that if Θ and s satisfy certain conditions, the embeddings Open image in new window , m/n+1/q−1/p>0 and Open image in new window , Φ being an Orlicz function subordinate to both φ(t)=|t|p exp |t|n/(n−m) and Φσ(t)=exp |t|σ−1, σ ⩾ 1, m/n>1/p, are of type ls. One result dealing with multiplications maps from Open image in new window into Lq(Θ) is also obtained.


Sobolev Space Unbounded Domain Orlicz Space Orlicz Function Piecewise Polynomial 
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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • J. A. S. Martins
    • 1
    • 2
  1. 1.England
  2. 2.CoimbraPortugal

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