Bourgain–Brezis inequalities on symmetric spaces of non-compact type

Sagun Chanillo; Jean Van Schaftingen; Po Lam Yung

doi:10.1016/j.jfa.2017.05.005

Bourgain–Brezis inequalities on symmetric spaces of non-compact type

Sagun Chanillo, Jean Van Schaftingen, Po Lam Yung^*

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

Let M be a global Riemannian symmetric space of non-compact type. We prove a duality estimate, for pairings of divergence-free L¹ vector fields, with vector fields in a critical Sobolev space on M: |∫M〈f,ϕ〉dV|≤C‖f‖_L¹(dV)‖∇ϕ‖_L^m(dV). This estimate provides a remedy for the failure of a critical Sobolev embedding on such symmetric spaces.

Original language	English
Pages (from-to)	1504-1547
Number of pages	44
Journal	Journal of Functional Analysis
Volume	273
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2017.05.005
Publication status	Published - 15 Aug 2017
Externally published	Yes

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title = "Bourgain–Brezis inequalities on symmetric spaces of non-compact type",

abstract = "Let M be a global Riemannian symmetric space of non-compact type. We prove a duality estimate, for pairings of divergence-free L1 vector fields, with vector fields in a critical Sobolev space on M: |∫M〈f,ϕ〉dV|≤C‖f‖L1(dV)‖∇ϕ‖Lm(dV). This estimate provides a remedy for the failure of a critical Sobolev embedding on such symmetric spaces.",

keywords = "Critical Sobolev space, Iwasawa decomposition, Lie group, Symmetric space",

author = "Sagun Chanillo and {Van Schaftingen}, Jean and Yung, {Po Lam}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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AU - Van Schaftingen, Jean

AU - Yung, Po Lam

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N2 - Let M be a global Riemannian symmetric space of non-compact type. We prove a duality estimate, for pairings of divergence-free L1 vector fields, with vector fields in a critical Sobolev space on M: |∫M〈f,ϕ〉dV|≤C‖f‖L1(dV)‖∇ϕ‖Lm(dV). This estimate provides a remedy for the failure of a critical Sobolev embedding on such symmetric spaces.

AB - Let M be a global Riemannian symmetric space of non-compact type. We prove a duality estimate, for pairings of divergence-free L1 vector fields, with vector fields in a critical Sobolev space on M: |∫M〈f,ϕ〉dV|≤C‖f‖L1(dV)‖∇ϕ‖Lm(dV). This estimate provides a remedy for the failure of a critical Sobolev embedding on such symmetric spaces.

KW - Critical Sobolev space

KW - Iwasawa decomposition

KW - Lie group

KW - Symmetric space

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U2 - 10.1016/j.jfa.2017.05.005

DO - 10.1016/j.jfa.2017.05.005

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SP - 1504

EP - 1547

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 4

ER -

Bourgain–Brezis inequalities on symmetric spaces of non-compact type

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