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

References in corpus (3)

• Convolutions of singular measures and applications to the Zakharov system
• Stability of the Brascamp-Lieb constant and applications
• The Endpoint Perturbed Brascamp-Lieb Inequality with Examples

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• Five-Linear Singular Integral Estimates of Brascamp-Lieb Type
• Decoupling inequalities for quadratic forms
• Regularized Brascamp--Lieb inequalities
• An Algebraic Brascamp-Lieb Inequality
• A new approach to the Fourier extension problem for the paraboloid