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Embeddings of Sobolev spaces of fractional order†

Published online by Cambridge University Press:  14 February 2012

J. S. Martins
J. S. Martins
Affiliation:
Department of Mathematics, University of Sussex and University of Coimbra, Portugal
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Synopsis

If Ω is a bounded domain in Rn satisfying certain conditions, Ωk denotes its intersection with a k-dimensional hyperplane, 1 ≦ k ≦ n, it is shown that the embedding of the Sobolev space Ws,p(Ω), s>0, into Lq(Ωk) is of type lm if for q<p<∞. The same result is obtained for the space of Bessel potentials Ls,p(Ω). Piecewise polynomial and Fourier approximations of functions and interpolation theorems areused.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 1-2 , 1977 , pp. 1 - 24
Copyright
Copyright © Royal Society of Edinburgh 1977

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