Displaying similar documents to “Approximation and entropy numbers of compact Sobolev embeddings”

Spaces of Lipschitz type, embeddings and entropy numbers

Edmunds D. E., Haroske D.

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AbstractWe establish the sharpness of the embedding of certain Besov and Triebel-Lizorkin spaces in spaces of Lipschitz type. In particular, this proves the sharpness of the Brézis-Wainger result concerning the “almost” Lipschitz continuity of elements of the Sobolev space H p 1 + n / p ( ℝ ⁿ ) , where 1 < p < ∞. Upper and lower estimates are obtained for the entropy numbers of related embeddings of Besov spaces on bounded domains. CONTENTSIntroduction...........................................................51....

Function spaces of generalised smoothness

Susana Domingues de Moura

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We study spaces of generalised smoothness of Besov and Triebel-Lizorkin type. In particular, we get characterisations by local means, atomic and subatomic representations. These results are applied to estimate the entropy numbers of compact embeddings between function spaces on fractals. Due to Carl's inequality this is useful in the study of the behaviour of eigenvalues in problems which correspond to the vibrations of a drum, the whole mass of which is concentrated on a fractal subset...

A new approach to mutual information

Fumio Hiai, Dénes Petz (2007)

Banach Center Publications

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A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.

On Entropy Bumps for Calderón-Zygmund Operators

Michael T. Lacey, Scott Spencer (2015)

Concrete Operators

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We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ℇ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on Rd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound [...]

Maličky-Riečan's entropy as a version of operator entropy

Bartosz Frej (2006)

Fundamenta Mathematicae

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The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.