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besov and triebel–lizorkin spaces

Proceedings of the Edinburgh Mathematical Society (1)

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Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators
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Hans-Gerd Leopold, Leszek Skrzypczak
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013

Published online by Cambridge University Press:

10 July 2013, pp. 829-851
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We prove sufficient and necessary conditions for compactness of the Sobolev embeddings of Besov and Triebel–Lizorkin spaces defined on bounded and unbounded uniformly E-porous domains. The asymptotic behaviour of the corresponding entropy numbers is calculated. Some applications to the spectral properties of elliptic operators are described.