Approximation in the Zygmund class

Artur Nicolau; Odí Soler i Gibert

doi:10.1112/jlms.12267

Approximation in the Zygmund class

Artur Nicolau, Odí Soler i Gibert

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4 Citations (Scopus)

Abstract

© 2019 London Mathematical Society We study the distance in the Zygmund class (Formula presented.) to the subspace (Formula presented.) of functions with distributional derivative with bounded mean oscillation. In particular, we describe the closure of (Formula presented.) in the Zygmund seminorm. We also generalise this result to Zygmund measures on (Formula presented.). Finally, we apply the techniques developed in the article to characterise the closure of the subspace of functions in (Formula presented.) that are also in the classical Sobolev space (Formula presented.), for (Formula presented.).

Original language	English
Journal	Journal of the London Mathematical Society
DOIs	https://doi.org/10.1112/jlms.12267
Publication status	Published - 1 Jan 2019

Keywords

26A16
26A24 (primary)

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10.1112/jlms.12267

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title = "Approximation in the Zygmund class",

abstract = "{\textcopyright} 2019 London Mathematical Society We study the distance in the Zygmund class (Formula presented.) to the subspace (Formula presented.) of functions with distributional derivative with bounded mean oscillation. In particular, we describe the closure of (Formula presented.) in the Zygmund seminorm. We also generalise this result to Zygmund measures on (Formula presented.). Finally, we apply the techniques developed in the article to characterise the closure of the subspace of functions in (Formula presented.) that are also in the classical Sobolev space (Formula presented.), for (Formula presented.).",

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author = "Artur Nicolau and {Soler i Gibert}, Od{\'i}",

year = "2019",

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doi = "10.1112/jlms.12267",

language = "English",

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T1 - Approximation in the Zygmund class

AU - Nicolau, Artur

AU - Soler i Gibert, Odí

PY - 2019/1/1

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N2 - © 2019 London Mathematical Society We study the distance in the Zygmund class (Formula presented.) to the subspace (Formula presented.) of functions with distributional derivative with bounded mean oscillation. In particular, we describe the closure of (Formula presented.) in the Zygmund seminorm. We also generalise this result to Zygmund measures on (Formula presented.). Finally, we apply the techniques developed in the article to characterise the closure of the subspace of functions in (Formula presented.) that are also in the classical Sobolev space (Formula presented.), for (Formula presented.).

AB - © 2019 London Mathematical Society We study the distance in the Zygmund class (Formula presented.) to the subspace (Formula presented.) of functions with distributional derivative with bounded mean oscillation. In particular, we describe the closure of (Formula presented.) in the Zygmund seminorm. We also generalise this result to Zygmund measures on (Formula presented.). Finally, we apply the techniques developed in the article to characterise the closure of the subspace of functions in (Formula presented.) that are also in the classical Sobolev space (Formula presented.), for (Formula presented.).

KW - 26A16

KW - 26A24 (primary)

UR - http://www.mendeley.com/research/approximation-zygmund-class

U2 - 10.1112/jlms.12267

DO - 10.1112/jlms.12267

M3 - Article

SN - 0024-6107

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

ER -

Approximation in the Zygmund class

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Aspectos probabilísticos y geométricos de la teoría de funciones

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Approximation in the Zygmund class

Abstract

Keywords

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Aspectos probabilísticos y geométricos de la teoría de funciones

Cite this