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

1 Scopus citations

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)
Pages (from-to)	260-278
Number of pages	19
Journal	Advanced Nonlinear Studies
Volume	25
Issue number	2
DOIs	https://doi.org/10.1515/ans-2023-0132
State	Published - Apr 1 2025

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
General Mathematics

Keywords

Calderón–Zygmund decomposition
Sobolev extension
Whitney extension
linear 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, Sobolev extension, Whitney extension, linear extension",

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

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T1 - Sobolev extension in a simple case

AU - Drake, Marjorie

AU - Fefferman, Charles

AU - Ren, Kevin

AU - Skorobogatova, Anna

PY - 2025/4/1

Y1 - 2025/4/1

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 - Sobolev extension

KW - Whitney extension

KW - linear extension

UR - https://www.scopus.com/pages/publications/85194061711

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

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DO - 10.1515/ans-2023-0132

M3 - Article

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SN - 1536-1365

VL - 25

SP - 260

EP - 278

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

IS - 2

ER -

Sobolev extension in a simple case

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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