Approximation of functions from Nikolskii–Besov type classes of generalized mixed smoothness

Stasyuk, S. A.; Yanchenko, S. Ya.

doi:10.1007/s10476-015-0305-0

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A Non-compactness Result In the Integer Case1

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2017

2024

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Cited by 7 publications

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“…If the question of how to approximate a given f ∈ B s p,q (R N ) in a "suitable manner" has already been well-studied (see e.g. [15,19,26]), to the author's knowledge it seems, however, that no criterion to recognize a function f ∈ B s p,∞ (R N ) which can be approximated by smooth functions in its natural (strong) topology is available in the literature.…”

Section: A Non-compactness Result In the Integer Casementioning

confidence: 99%

A Bourgain–Brezis–Mironescu characterization of higher order Besov–Nikol^{\prime }skii spaces

Brasseur¹

2018

Ann. inst. Fourier

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We study a class of nonlocal functionals in the spirit of the recent characterization of the Sobolev spaces W 1,p derived by Bourgain, Brezis and Mironescu. We show that it provides a common roof to the description of the BV (R N ), W 1,p (R N ), B s p,∞ (R N ) and C 0,1 (R N ) scales and we obtain new equivalent characterizations for these spaces. We also establish a noncompactness result for sequences and new (non-)limiting embeddings between Lipschitz and Besov spaces which extend the previous known results.2010 Mathematics Subject Classification. 46E35.

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Section: A Non-compactness Result In the Integer Casementioning

confidence: 99%

A Bourgain–Brezis–Mironescu characterization of higher order Besov–Nikol^{\prime }skii spaces

Brasseur¹

2018

Ann. inst. Fourier

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show abstract

Constructive sparse trigonometric approximations for the functions with generalized mixed smoothness

Stasyuk

2017

J Math Sci

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Approximative characteristics of functions from the classes S p , θ Ω $$ {S}_{p,\theta}^{\varOmega } $$ B(ℝd) with a given majorant of mixed moduli of continuity

Yanchenko

Stasyuk

2018

J Math Sci

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Approximation of functions from Nikolskii–Besov type classes of generalized mixed smoothness

Cited by 7 publications

References 5 publications

A Bourgain–Brezis–Mironescu characterization of higher order Besov–Nikol^{\prime }skii spaces

A Bourgain–Brezis–Mironescu characterization of higher order Besov–Nikol^{\prime }skii spaces

Constructive sparse trigonometric approximations for the functions with generalized mixed smoothness

Approximative characteristics of functions from the classes S p , θ Ω $$ {S}_{p,\theta}^{\varOmega } $$ B(ℝd) with a given majorant of mixed moduli of continuity

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