Compact embeddings between Besov spaces defined on $h$-sets

Bricchi, Michele

doi:10.7169/facm/1538186659

Cited by 7 publications

(2 citation statements)

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“…It is known that an admissible function is, up to equivalence, a slowly varying function. This is proved in [2], see also [3,Proposition 4.16]. Hence an admissible function need not to be slowly varying, but there is always an equivalent slowly varying representative.…”

Section: Slowly Varying Functions and Hardy Inequalitiesmentioning

confidence: 97%

Compact embeddings of Sobolev spaces with power weights perturbed by slowly varying functions

Mieth

2015

Math. Nachr.

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Key words Weighted Sobolev spaces, entropy numbers, approximation numbers, degenerate elliptic operators, continuous and compact embeddings, slowly varying functions, quadratic forms MSC (2010) 46E35We study compact embeddings of weighted Sobolev spaces into Lebesgue spaces on the unit ball in R n . The weight is of slowly varyingly disturbed polynomial growth with a singularity at the origin. It extends [21], [27] to a wider class of weights. Special attention is paid to the influence of the growth rate of the weight on the quality of compactness, measured in terms of entropy and approximation numbers. In case of Hilbert spaces, the results are related to the distribution of eigenvalues of some degenerate elliptic operators.

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Section: Slowly Varying Functions and Hardy Inequalitiesmentioning

confidence: 97%

Compact embeddings of Sobolev spaces with power weights perturbed by slowly varying functions

Mieth

2015

Math. Nachr.

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“…We now study embedding assertions of type B σ p,q (Γ) ֒→ L r (Γ) and B σ p 1 ,q 1 (Γ) ֒→ B τ p 2 ,q 2 (Γ) . In contrast to previous considerations in [6], see also [4], we are especially interested in 'sharp' embeddings, that is, to give necessary and sufficient conditions for the existence of such embeddings, whereas in the above-mentioned papers the focus was rather on the compactness of related embeddings.…”

Section: 2mentioning

confidence: 99%

Embeddings of Besov spaces on fractal $h$-sets

Caetano¹,

Haroske²

2015

Banach J. Math. Anal.

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Let Γ be a fractal h-set and B σ p,q (Γ) be a trace space of Besov type defined on Γ. While we dealt in [9] with growth envelopes of such spaces mainly and investigated the existence of traces in detail in [12], we now study continuous embeddings between different spaces of that type on Γ. We obtain necessary and sufficient conditions for such an embedding to hold, and can prove in some cases complete characterisations. It also includes the situation when the target space is of type L r (Γ) and, as a by-product, under mild assumptions on the h-set Γ we obtain the exact conditions on σ, p and q for which the trace space B σ p,q (Γ) exists. We can also refine some embedding results for spaces of generalised smoothness on R n .

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The Fractal Laplacian and Multifractal Quantities

Triebel

2004

Fractal Geometry and Stochastics III

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Compact embeddings between Besov spaces defined on $h$-sets

Cited by 7 publications

References 0 publications

Compact embeddings of Sobolev spaces with power weights perturbed by slowly varying functions

Compact embeddings of Sobolev spaces with power weights perturbed by slowly varying functions

Embeddings of Besov spaces on fractal $h$-sets

The Fractal Laplacian and Multifractal Quantities

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