A Variation on H\"older-Brascamp-Lieb Inequalities
Classical Analysis and ODEs
2017-11-23 v2
Abstract
The H\"older-Brascamp-Lieb inequalities are a collection of multilinear inequalities generalizing a convolution inequality of Young and the Loomis-Whitney inequalities. The full range of exponents was classified in Bennett et al. (2008). In a setting similar to that of Ivanisvili and Volberg (2015), we introduce a notion of size for these inequalities which generalizes norms. Under this new setup, we then determine necessary and sufficient conditions for a generalized H\"older-Brascamp-Lieb type inequality to hold and establish sufficient conditions for extremizers to exist when the underlying linear maps match those of the convolution inequality of Young.
Keywords
Cite
@article{arxiv.1710.06374,
title = {A Variation on H\"older-Brascamp-Lieb Inequalities},
author = {Kevin O'Neill},
journal= {arXiv preprint arXiv:1710.06374},
year = {2017}
}
Comments
November update to clarify an argument in Section 3