论文标题
关于仿射不变和本地Loomis-Whitney类型不平等现象
On affine invariant and local Loomis-Whitney type inequalities
论文作者
论文摘要
我们证明了Loomis-Whitney不平等及其双重的各种扩展，在这些扩展是由向量（或部分）跨越的子空间，或者要么由vectors $ w_i $跨越，不一定是$ \ mathbb {r}^n $的正常基础的$ w_i $。为了证明这种不平等现象，我们根据向量$ w_i $估计Brascamp-Lieb不平等的常数。不平等的限制和功能版本也将被考虑。
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 $\mathbb{R}^n$, 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.
