Premium
On affine invariant and local Loomis–Whitney type inequalities
Author(s) -
AlonsoGutiérrez David,
Bernués Julio,
Brazitikos Silouanos,
Carbery Anthony
Publication year - 2021
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12411
Subject(s) - orthonormal basis , linear subspace , mathematics , inequality , invariant (physics) , affine transformation , pure mathematics , combinatorics , mathematical analysis , physics , quantum mechanics , mathematical physics
We prove various extensions of the Loomis–Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors w i of a not necessarily orthonormal basis of R n , or their orthogonal complements. In order to prove such inequalities, we estimate the constant in the Brascamp–Lieb inequality in terms of the vectors w i . Restricted and functional versions of the inequality will also be considered.