Variations on a proof of a borderline Bourgain-Brezis Sobolev embedding theorem

Abstract

We offer a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on ${\mathbb{R}}^n$. We use this idea to extend the result to real hyperbolic spaces ${\mathbb{H}}^n$.

21 pages; to appear in a Special Issue of Chinese Annals of Mathematics in honour of Haim Brezis

Cited by in corpus (4)

• Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type
• Applications of Bourgain-Brezis inequalities to Fluid Mechanics and Magnetism
• Injective ellipticity, cancelling operators, and endpoint Gagliardo-Nirenberg-Sobolev inequalities for vector fields
• Endpoint Sobolev inequalities for vector fields and cancelling operators