scholarly journals Trace operators on fractals, entropy and approximation numbers

2011 ◽  
Vol 18 (3) ◽  
pp. 549-575
Author(s):  
Cornelia Schneider
Keyword(s):  
Besov Spaces ◽  
Trace Operator ◽  
Approximation Numbers ◽  
Atomic Decompositions ◽  
Sharp Estimates ◽  
Compact Embeddings ◽  
Trace Space

Abstract First we compute the trace space of Besov spaces – characterized via atomic decompositions – on fractals Γ, for parameters 0 < p < ∞, 0 < q ≤ min(1, p) and s = (n – d)/p. New Besov spaces on fractals are defined via traces for 0 < p, q ≤ ∞, s ≥ (n – d)/p and some embedding assertions are established. We conclude by studying the compactness of the trace operator TrΓ by giving sharp estimates for entropy and approximation numbers of compact embeddings between Besov spaces. Our results on Besov spaces remain valid considering the classical spaces defined via differences. The trace results are used to study traces in Triebel–Lizorkin spaces as well.

Compact embeddings of some weighted Sobolev spaces on ℝN

1995 ◽  
Vol 117 (2) ◽  
pp. 333-338 ◽  
Author(s):  
Raffaele Chiappinelli
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Compact Embeddings ◽  
Measurable Functions ◽  
Image Position

Let ρ,ρ0,ρ1 be positive, measurable functions on ℝN. For 1 ≤ t < ∞, consider the weighted Lebesgue and Sobolev spaces

scholarly journals Compact embeddings of the space of functions with bounded logarithmic deformation

2010 ◽  
Vol 172 (1) ◽  
pp. 165-183 ◽  
Author(s):  
M. Fuchs ◽  
M. Bildhauer
Keyword(s):  
Compact Embeddings

Almost-compact embeddings

2012 ◽  
pp. n/a-n/a
Author(s):  
Lenka Slavíková
Keyword(s):  
Compact Embeddings

Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications

2002 ◽  
Vol 9 (3) ◽  
pp. 567-590
Author(s):  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Entropy Numbers ◽  
Compact Embeddings

Abstract The author first establishes the frame characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type. As applications, the author then obtains some estimates of entropy numbers for the compact embeddings between Besov spaces or between Triebel–Lizorkin spaces. Moreover, some real interpolation theorems on these spaces are also established by using these frame characterizations and the abstract interpolation method.

Embeddings of weighted Sobolev spaces into spaces of continuous functions

1992 ◽  
Vol 439 (1906) ◽  
pp. 279-296 ◽  
Keyword(s):  
Weighted Sobolev Spaces ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Hölder Continuous ◽  
Compact Embeddings ◽  
Spaces Of Continuous Functions ◽  
Hölder Continuous Functions ◽  
Continuous And Compact Embeddings ◽  
Necessary And Sufficient ◽  
Theoretical Results

We give sufficient conditions and necessary conditions (which in some cases are both necessary and sufficient) for continuous and compact embeddings of the weighted Sobolev space W 1,p ( Ω ;v 0 v 1 )into spaces of weighted continuous and Holder continuous functions. The theoretical results are illustrated by several examples.

Subradial functions and compact embeddings

2014 ◽  
Vol 284 (1) ◽  
pp. 216-234
Author(s):  
Winfried Sickel ◽  
Leszek Skrzypczak
Keyword(s):  
Compact Embeddings
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