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.

arXiv comment8 pages. Author accepted version. To appear in Bull. London Math. Soc

References in corpus (4)

• On a reverse form of the Brascamp-Lieb inequality
• 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