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

Sagun Chanillo, Jean Van Schaftingen, Po Lam Yung

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1504-1547
Number of pages44
JournalJournal of Functional Analysis
Volume273
Issue number4
DOIs
StatePublished - Aug 15 2017

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Critical Sobolev space
  • Iwasawa decomposition
  • Lie group
  • Symmetric space

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