Sobolev extension in a simple case

Marjorie Drake; Charles Fefferman; Kevin Ren; Anna Skorobogatova

doi:10.1515/ans-2023-0132

Sobolev extension in a simple case

Marjorie Drake, Charles Fefferman, Kevin Ren, Anna Skorobogatova

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we establish the existence of a bounded, linear extension operator T: L^{2, p} (E) → L^{2, p} (R²) when 1 < p < 2 and E is a finite subset of R² contained in a line.

Original language	English (US)
Journal	Advanced Nonlinear Studies
DOIs	https://doi.org/10.1515/ans-2023-0132
State	Accepted/In press - 2024

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
General Mathematics

Keywords

Calderón-Zygmund decomposition
linear extension
Sobolev extension
Whitney extension

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10.1515/ans-2023-0132

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title = "Sobolev extension in a simple case",

abstract = "In this paper, we establish the existence of a bounded, linear extension operator T: L2, p (E) → L2, p (R2) when 1 < p < 2 and E is a finite subset of R2 contained in a line.",

keywords = "Calder{\'o}n-Zygmund decomposition, linear extension, Sobolev extension, Whitney extension",

author = "Marjorie Drake and Charles Fefferman and Kevin Ren and Anna Skorobogatova",

note = "Publisher Copyright: {\textcopyright} 2024 the author(s), published by De Gruyter, Berlin/Boston 2024.",

year = "2024",

doi = "10.1515/ans-2023-0132",

language = "English (US)",

journal = "Advanced Nonlinear Studies",

issn = "1536-1365",

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T1 - Sobolev extension in a simple case

AU - Drake, Marjorie

AU - Fefferman, Charles

AU - Ren, Kevin

AU - Skorobogatova, Anna

PY - 2024

Y1 - 2024

N2 - In this paper, we establish the existence of a bounded, linear extension operator T: L2, p (E) → L2, p (R2) when 1 < p < 2 and E is a finite subset of R2 contained in a line.

AB - In this paper, we establish the existence of a bounded, linear extension operator T: L2, p (E) → L2, p (R2) when 1 < p < 2 and E is a finite subset of R2 contained in a line.

KW - Calderón-Zygmund decomposition

KW - linear extension

KW - Sobolev extension

KW - Whitney extension

UR - http://www.scopus.com/inward/record.url?scp=85194061711&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85194061711&partnerID=8YFLogxK

U2 - 10.1515/ans-2023-0132

DO - 10.1515/ans-2023-0132

M3 - Article

AN - SCOPUS:85194061711

SN - 1536-1365

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

ER -

Sobolev extension in a simple case

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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