A subelliptic Bourgain-Brezis inequality

Yi Wang; Po Lam Yung

doi:10.4171/JEMS/443

A subelliptic Bourgain-Brezis inequality

Yi Wang, Po Lam Yung

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

7 Citations (Scopus)

Abstract

We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space NL ^1,Q by L∞ functions, generalizing a result of Bourgain-Brezis [BB2]. We then use this to obtain a Gagliardo-Nirenberg inequality for δ_b on the Heisenberg group Hⁿ.

Original language	English
Pages (from-to)	649-693
Number of pages	45
Journal	Journal of the European Mathematical Society
Volume	16
Issue number	4
DOIs	https://doi.org/10.4171/JEMS/443
Publication status	Published - 2014
Externally published	Yes

Access to Document

10.4171/JEMS/443

Cite this

@article{6efa8bc309f246fb90d3824fb35b5052,

title = "A subelliptic Bourgain-Brezis inequality",

abstract = "We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space NL 1,Q by L∞ functions, generalizing a result of Bourgain-Brezis [BB2]. We then use this to obtain a Gagliardo-Nirenberg inequality for δb on the Heisenberg group Hn.",

keywords = "Compensation phenomena, Critical Sobolev embedding, Div-curl, Homogeneous groups",

author = "Yi Wang and Yung, {Po Lam}",

year = "2014",

doi = "10.4171/JEMS/443",

language = "English",

volume = "16",

pages = "649--693",

journal = "Journal of the European Mathematical Society",

issn = "1435-9855",

publisher = "European Mathematical Society Publishing House",

number = "4",

}

TY - JOUR

T1 - A subelliptic Bourgain-Brezis inequality

AU - Wang, Yi

AU - Yung, Po Lam

PY - 2014

Y1 - 2014

N2 - We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space NL 1,Q by L∞ functions, generalizing a result of Bourgain-Brezis [BB2]. We then use this to obtain a Gagliardo-Nirenberg inequality for δb on the Heisenberg group Hn.

AB - We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space NL 1,Q by L∞ functions, generalizing a result of Bourgain-Brezis [BB2]. We then use this to obtain a Gagliardo-Nirenberg inequality for δb on the Heisenberg group Hn.

KW - Compensation phenomena

KW - Critical Sobolev embedding

KW - Div-curl

KW - Homogeneous groups

UR - http://www.scopus.com/inward/record.url?scp=84898023001&partnerID=8YFLogxK

U2 - 10.4171/JEMS/443

DO - 10.4171/JEMS/443

M3 - Article

AN - SCOPUS:84898023001

SN - 1435-9855

VL - 16

SP - 649

EP - 693

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 4

ER -

A subelliptic Bourgain-Brezis inequality

Abstract

Access to Document

Other files and links

Fingerprint

Cite this