论文标题
Banach空间中的Subgaussian Kahane-Salem-Zygmund不平等现象
Subgaussian Kahane-Salem-Zygmund inequalities in Banach spaces
论文作者
论文摘要
这项工作的主要目的是为著名的Kahane-Salem-Zygmund的不平等现象提供一般方法。我们证明了平均指数orlicz规范的估计值$ \ sup_ {1 \ le j \ leq n} \ big | \ sum_ {1 \ leq i \ leq i \ leq k}γ_i（\ cdot）a_ {i，j} $（γ_i）$一系列真实或复杂的Subgauss随机变量。将这些不平等提升为有限的尺寸Banach空间，我们得到了新颖的Kahane-Salem-Zygmund型不平等，特别是在有限的尺寸尺寸Banach空间以及Subgaussian Random Dirichlet dirichlet dirichlet Polynomials上，在有限尺寸的Banach空间上，船长随机多项式和多线性形式的空间。最后，我们使用抽象的插值理论大大扩展了我们的方法。
The main aim of this work is to give a general approach to the celebrated Kahane-Salem-Zygmund inequalities. We prove estimates for exponential Orlicz norms of averages $\sup_{1\le j \leq N} \big |\sum_{1 \leq i \leq K}γ_i(\cdot) a_{i,j}\big|$ where $(a_{i,j})$ denotes a matrix of scalars and the $(γ_i)$ a sequence of real or complex subgaussian random variables. Lifting these inequalities to finite dimensional Banach spaces, we get novel Kahane-Salem-Zygmund type inequalities -- in particular, for spaces of subgaussian random polynomials and multilinear forms on finite dimensional Banach spaces as well as subgaussian random Dirichlet polynomials. Finally, we use abstract interpolation theory to widen our approach considerably.
