Multilinear Hölder-type inequalities on Lorentz sequence spaces

多线性卷积算子的洛伦兹估计

Lorentz estimates for multilinear convolution operators

该论文研究两类多线性卷积算子的洛伦兹估计，补充弱核理论、改进多线性Young不等式，推广Hörmander条件并构造反例，获特殊核的正结果。

Diagonal Multilinear Operators on Köthe Sequence Spaces

We analyze the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated Köthe sequence spaces. We establish relationships with spaces of multipliers and apply these results to describe diagonal multilinear operators from Lorentz sequence spaces. We also define and study some properties of the ideal of $(E;p)$-summing multilinear mappings, a natural extension of the linear ideal of absolutely $(E;p)$-summing operators.

球 Banach 函数空间上关于多重线性 Calderón-Zygmund 算子的 Hardy 空间弱分解

Weak Factorizations of the Hardy Spaces in Terms of Multilinear Calderón-Zygmund Operators on Ball Banach Function Spaces

本文在球 Banach 函数空间上基于多重线性 Calderón-Zygmund 算子建立了经典 Hardy 空间的弱分解，并通过该算子生成交换子的有界性获得了 BMO 空间的新刻画，结果可应用于多种函数空间。

Contraction and decoupling inequalities for multilinear forms and u-statistics

We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz norms), tail distributions, tightness, hypercontractivity, etc.

Bohnenblust-Hille inequalities for Lorentz spaces via interpolation

We prove that the Lorentz sequence space $\ell_{\frac{2m}{m+1},1}$ is, in a~precise sense, optimal among all symmetric Banach sequence spaces satisfying a Bohnenblust-Hille type inequality for $m$-linear forms or $m$-homogeneous polynomials on $\mathbb{C}^n$. Motivated by this result we develop methods for dealing with subtle Bohnenblust-Hille type inequalities in the setting of Lorentz spaces. Based on an interpolation approach and the Blei-Fournier inequalities involving mixed type spaces, we prove multilinear and polynomial Bohnenblust-Hille type inequalities in Lorentz spaces with subpolyn…

Hardy 型空间估计：多线性分数次积分算子

Hardy type spaces estimates for multilinear fractional integral operators

本文证明了多线性分数次积分算子在多种广义 Hardy 空间上的有界性，并推广了现有理论。