Behaviour of the Brascamp--Lieb constant

Abstract

Recent progress in multilinear harmonic analysis naturally raises questions about the local behaviour of the best constant (or bound) in the general Brascamp--Lieb inequality as a function of the underlying linear transformations. In this paper we prove that this constant is continuous, but is not in general differentiable.

8 pages. Author accepted version. To appear in Bull. London Math. Soc