Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities

By Jonathan Bennett, Anthony Carbery, Michael Christ, Terence Tao. 2005

130 citations recorded by the source corpus.

A criterion is established for the validity of multilinear inequalities of a class considered by Brascamp and Lieb, generalizing well-known inequalties of Rogers and H\"older, Young, and Loomis-Whitney.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7c605d54c5c4dbabf9c93ac9b9f3353100accbad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Discrete Mathematics and Combinatorics

In Numerical Analysis

Citations in the corpus

Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, unknown): “We recall the following theorem from [2].”
Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, background): “The finiteness condition (46) is somewhat difficult to interpret in general, although under certain 11For closely related multilinear oscillatory integral inequalities, that may also be viewed as oscillatory Brascamp–Lieb inequalities, see [26], [25] and [12].”
Communication lower bounds and optimal algorithms for programs that reference arrays - Part 1 (2013, methodology): “A similar algorithm was sketched in [25] for computing the polytope in [6, Theorem 2.1], a result related to Theorem 3.10 in the case F = R but where the vector spaces V, V j are endowed with additional inner-product structure.”
Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities (2007, methodology): “Bennett, Carbery, Christ and Tao [ BeCCT1 ] used a similar approach to deal with the multi-dimensional versions of the Brascamp– Lieb inequality (see also [BeCCT2] for a direct approach to the finiteness of the constant eD).”