论文标题
非阳性操作员的分离，多线性二元性和分解
Disentanglement, Multilinear Duality and Factorisation for non-positive operators
论文作者
论文摘要
在先前的工作中，我们建立了针对定义晶格定义的正线性算子的指定加权几何平均值的规范不平等的多线性双重性和分解理论。在本文中，我们首次将理论的影响范围扩展到了在规范空间上定义的一般线性操作员的设置。该理论的范围包括多线性傅立叶限制型不平等。我们还提高了先前的积极运营者理论。 我们的结果都共有一个共同的主题：对线性运算符的加权几何平均值的估计可以分别对每个运算符的定量估计值分开。整个论文均出现了解散的概念。 我们在先前工作中使用的方法 - 主要是凸优化 - 强烈依赖于阳性。相比之下，在本文中，我们使用了分离的矢量值重新制定，基础规范空间的几何特性（Rademacher型）以及与P稳定随机变量相关的概率考虑因素。
In previous work we established a multilinear duality and factorisation theory for norm inequalities for pointwise weighted geometric means of positive linear operators defined on normed lattices. In this paper we extend the reach of the theory for the first time to the setting of general linear operators defined on normed spaces. The scope of this theory includes multilinear Fourier restriction-type inequalities. We also sharpen our previous theory of positive operators. Our results all share a common theme: estimates on a weighted geometric mean of linear operators can be disentangled into quantitative estimates on each operator separately. The concept of disentanglement recurs throughout the paper. The methods we used in the previous work - principally convex optimisation - relied strongly on positivity. In contrast, in this paper we use a vector-valued reformulation of disentanglement, geometric properties (Rademacher-type) of the underlying normed spaces, and probabilistic considerations related to p-stable random variables.
