Year: 2018
Type: preprint
Abstract: We establish a nonlinear generalisation of the classical Brascamp-Lieb inequality in the case where the Lebesgue exponents lie in the interior of the finiteness polytope. As a corollary we show that the best constant in Young's convolution inequality in a small neighbourhood of the identity of a general Lie group, approaches the euclidean constant as the size of the neighbourhood approaches zero, answering a question of Cowling, Martini, Müller and Parcet. Our proof consists of running an efficient, or "tight", induction on scales argument which uses the existence of gaussian extremisers to the underlying linear Brascamp-Lieb inequality in a fundamental way.
Source: arXiv (Cornell University)
Institutions: Saitama University, University of Massachusetts Amherst
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2782829806