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

Chanillo, Sagun; Van Schaftingen, Jean; Yung, Po Lam

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

Date

2017-08-15

Authors

Chanillo, Sagun

Van Schaftingen, Jean

Yung, Po Lam

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.