Behaviour of the Brascamp--Lieb constant
Jonathan Bennett, Neal Bez, Michael G. Cowling, and Taryn C. Flock
TL;DR
This paper investigates the local behavior of the Brascamp--Lieb constant, establishing its continuity and non-differentiability as a function of the underlying linear transformations, advancing understanding in multilinear harmonic analysis.
Contribution
It proves the continuity and non-differentiability of the Brascamp--Lieb constant with respect to the linear transformations involved.
Findings
The Brascamp--Lieb constant is continuous as a function of the linear transformations.
The Brascamp--Lieb constant is not generally differentiable.
Advances understanding of the behavior of multilinear inequalities.
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.
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