scholarly journals s-numbers of compact embeddings of function spaces on quasi-bounded domains

2014 ◽  
Vol 30 (4) ◽  
pp. 495-513 ◽  
Author(s):  
Shun Zhang ◽  
Alicja Dota
Keyword(s):  
Function Spaces ◽  
Bounded Domains ◽  
Compact Embeddings

scholarly journals Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

2016 ◽  
Vol 146 (5) ◽  
pp. 905-927 ◽  
Author(s):  
António Caetano ◽  
Amiran Gogatishvili ◽  
Bohumír Opic
Keyword(s):  
Besov Spaces ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Banach Function Spaces ◽  
Compact Embeddings ◽  
Type Spaces ◽  
Besov Type Spaces

There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces Lp(ℝn), 1 ⩽ p < ∞, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces , into Lorentz-type spaces.

Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators

2013 ◽  
Vol 56 (3) ◽  
pp. 829-851 ◽  
Author(s):  
Hans-Gerd Leopold ◽  
Leszek Skrzypczak
Keyword(s):  
Asymptotic Behaviour ◽  
Spectral Properties ◽  
Necessary Conditions ◽  
Function Spaces ◽  
Elliptic Operators ◽  
Bounded Domains ◽  
Entropy Numbers ◽  
Sobolev Embeddings ◽  
Distribution Of Eigenvalues ◽  
Sufficient And Necessary Conditions

AbstractWe 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.

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