Some polynomial versions of cotype and applications

拟赋范空间的因子分解定理

Factorization theorems for quasi-normed spaces

本文将Pisier的抽象形式的Grothendieck定理推广到一般的非局部凸拟巴拿赫空间.证明了关于巴拿赫空间上的因子分解算子的一个相关结果，并将所得结果应用于Sidon集的向量值不等式的研究.我们还发展了弱余型为2的非局部凸空间的局部理论。

量子化规范正交系：一个非对易的Kwapiesten定理

Quantized orthonormal systems: A non-commutative Kwapień theorem

将给定巴拿赫空间的Riesz型和余型的概念推广到非交换情形。首先，将巴拿赫空间替换为算子空间。定义了量子化规范正交系的概念，它在经典环境中起着规范正交系的作用。一个算子空间关于一个非交换紧群的傅立叶型和余型就适合于这种情况。此外，Rademacher和高斯系统的量化类似的处理。所有这一切都是用来获得一个算子空间版本的经典定理的Kwapieste特征希尔伯特空间的向量值正交级数。几种方法，这一结果与不同的后果。

非线性谱隙的一种组合方法

A combinatorial approach to nonlinear spectral gaps

针对非线性谱隙的定量估计问题，提出基于正则图长程扩张性质的新颖组合框架，证明Poincaré常数对余型q的依赖为最优的多项式级别，并推广了随机图低失真嵌入的下界结果。

强鞅型与一致光滑性

Strong martingale type and uniform smoothness

本文引入了巴拿赫空间X的鞅型p <= 2和余型q >= 2的较强形式，并证明了这些概念分别等价于一致p-光滑性和q-凸性.所有这些都是度量概念，因此它们依赖于X中的特定范数。这些概念使我们能够更深入地了解X同构于一致p-光滑空间或X本身一致p-光滑之间的细微差别。我们不去研究Banach空间，而是直接考虑巴拿赫空间之间的线性算子。巴拿赫空间X的情形可以通过考虑X的恒等映射而由此重新发现。

Decoupling inequalities with exponential constants

Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued homogeneous polynomials evaluated at random variables. We focus on providing geometric conditions ensuring decoupling inequalities with good constants depending only exponentially on the degree of the polynomial. Assuming the Banach space has finite cotype we achieve this for classical decoupling inequalities that compare the polynomials with their associate…

Vector-valued local approximation spaces

We prove that for every Banach space $Y$, the Besov spaces of functions from the $n$-dimensional Euclidean space to $Y$ agree with suitable local approximation spaces with equivalent norms. In addition, we prove that the Sobolev spaces of type $q$ are continuously embedded in the Besov spaces of the same type if and only if $Y$ has martingale cotype $q$. We interpret this as an extension of earlier results of Xu (1998), and Martínez, Torrea and Xu (2006). These two results combined give the characterization that $Y$ admits an equivalent norm with modulus of convexity of power type $q$ if and o…

Banach空间中的离散对数Sobolev不等式

Discrete logarithmic Sobolev inequalities in Banach spaces

本文在有限余型Banach空间上建立了离散超立方体上与维数无关的向量值Lp对数Sobolev不等式，并利用该不等式给出Hamming立方体非线性商的双Lipschitz畸变新下界。

多项式环上希尔伯特模的高斯 - 博内 - 陈公式的阿夫森版本

Arveson's version of the Gauss-Bonnet-Chern formula for Hilbert modules over the polynomial rings

研究多项式环上希尔伯特模的高斯 - 博内 - 陈公式的阿夫森版本，通过证明局部代数子模与商模公式成立的等价性完善框架，建立渐近不变量和特征得到多变量类似公式，解决了\(H^2\)子模的有限缺陷问题。

The $p$-Bohr radius for vector-valued holomorphic and pluriharmonic functions

We study a "$p$-powered" version $K_n^p(F(R))$ of the well-known Bohr radius problem for the family $F(R)$ of holomorphic functions $f: R\to X$ satisfying $\|f\|<\infty$, where $\|.\|$ is a norm in the function space $F(R)$, $R\subset\mathbb{C}^n$ is a complete Reinhardt domain and $X$ is a complex Banach space. For all $p>0$, we describe in full details the asymptotic behaviour of $K_n^p(F(R))$, where $F(R)$ is (a) the Hardy space of $X$-valued holomorphic functions defined in the open unit polydisk $\mathbb{D}^n$, and (b) the space of bounded $X$-valued holomorphic or complex-valued plurihar…

Positive Polynomials on Riesz Spaces

We prove some properties of positive polynomial mappings between Riesz spaces, using finite difference calculus. We establish the polynomial analogue of the classical result that positive, additive mappings are linear. And we prove a polynomial version of the Kantorovich extension theorem.

多元正交多项式。I

Orthogonal polynomials in several variables. I

本文引入并讨论了几类多元非交换正交多项式。重点是一个非交换版本的正交多项式的实数线。我们介绍这些多项式的递归方程，Christoffel-Darboux公式和Jacobi型矩阵。

infinite dimensional空间上的控制多项式

Dominated polynomials on infinite dimensional spaces

本文的目的是证明任意无限维巴拿赫空间上存在非支配标量值m-齐次多项式（m>=3）的猜想的一个更强的版本.

代数基本定理的Banach代数化

A Banach Algebraic Version Of The Fundamental Theorem of Algebra

对于复巴拿赫代数中系数为的首一多项式p（z），证明了存在一个复数z使得p（z）不可逆

On the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality on bi-disc

Using the method of Rudin-Shapiro polynomials we prove the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality for complex partial differential operators with constant coefficients on bi-disc.