多重线性映像的可和性：Littlewood，Orlicz及以后

Domination spaces and factorization of linear and multilinear summing operators

It is well known that not every summability property for non linear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. We analyze the class of linear operators that are defined by a summability inequality involving a homogeneous map. Our construction includes the cases of absolutely $p$-summing linear operators, $(p,σ)$-absolutely continuous linear operat…

Riesz multiplier convergent spaces of operator valued series and a version of Orlicz- Pettis theorem

It is not usual to characterize an operator valued series via completeness of multiplier spaces. In this study, by using a series of bounded linear operators, we introduce the space $M^\infty_{R}\big(\sum_k T_k\big)$ of Riesz summability which is a generalization of the Cesàro summability. Therefore, we give the completeness criteria of these spaces with $c_0(X)$-multiplier convergent operator series. It is a natural consequence that one can characterize the completeness of a normed space through $M^\infty_{R}\big(\sum_k T_k\big)$ which will be assumed that is complete for every $c_0(X)$-multi…

求和多重线性映像的重合结果

Coincidence results for summing multilinear mappings

本文证明了巴拿赫空间之间绝对和多重线性映像空间的重合结果。这些结果的性质产生于两个不同的方法：两个\textit{a priori}不同类的求和多重线性映像的重合和所有多重线性映像定义在巴拿赫空间的产品的可求和性。已知结果的最佳推广。我们还介绍和探索在该领域的新技术，例如一种技术，以延长符合结果的线性，双线性，甚至三线性映射一般多线性的。

Summability of multilinear forms on classical sequence spaces

We present an extension of the Hardy--Littlewood inequality for multilinear forms. More precisely, let $\mathbb{K}$ be the real or complex scalar field and $m,k$ be positive integers with $m\geq k\,$ and $n_{1},\dots ,n_{k}$ be positive integers such that $n_{1}+\cdots +n_{k}=m$. ($a$) If $(r,p)\in (0,\infty )\times \lbrack 2m,\infty ]$ then there is a constant $D_{m,r,p,k}^{\mathbb{K}}\geq 1$ (not depending on $n$) such that $$ \left( \sum_{i_{1},\dots ,i_{k}=1}^{n}\left| T\left( e_{i_{1}}^{n_{1}},\dots ,e_{i_{k}}^{n_{k}}\right) \right| ^{r}\right) ^{% \frac{1}{r}}\leq D_{m,r,p,k}^{\mathbb{K}…

指定组合维数支集上的尖锐可和性

Sharp Summability on Supports of Prescribed Combinatorial Dimension

本文解决了Bayart框架中两个尖锐性问题：确定了指定组合维数支集的最优乘积可和性指数，并构造了一个单一无限支集，在Hilbert阈值上下同时达到最优Hardy--Littlewood指数，揭示了维数依赖性的转变。

关于非线性映射的可和性：一种新方法

On summability of nonlinear mappings: a new approach

本文的主要目的是刻画巴拿赫空间之间的任意非线性（非多线性）映射$f:X_{1}\times...\times X_{n}\rightarrow Y$，该映射满足围绕给定点$(a_{1},...,a_{n})\in$ $X_{1}\times...\times X_{n}$的一个非常自然的Pietsch控制型定理.由于我们的方法的加权求和的概念自然产生，这可能是一个有趣的话题，进一步调查。

Lipschitz $p$-summing multilinear operators

We apply the geometric approach provided by $Σ$-operators to develop a theory of $p$-summability for multilinear operators. In this way, we introduce the notion of Lipschitz $p$-summing multilinear operators and show that it is consistent with a general panorama of generalization: Namely, they satisfy Pietsch-type domination and factorization theorems and generalizations of the inclusion Theorem, Grothendieck's coincidence Theorems, the weak Dvoretsky-Rogers Theorem and a Lindenstrauss-Pelczyńsky Theorem. We also characterize this new class in tensorial terms by means of a Chevet-Saphar-type t…

Regularity of the coefficients of multilinear forms on sequence spaces

The investigation of regularity/summability properties of the coefficients of bilinear forms in sequence spaces was initiated by Littlewood in $1930$. Nowadays, this topic has important connections with other fields of Pure and Applied Mathematics as Complex Analysis, Quantum Information Theory, Theoretical Computer Science and Combinatorial Games. In this paper we explore a regularity technique to obtain optimal parameters for several results in this framework, extending/generalizing theorems of Osikiewicz and Tonge ($2001$), Albuquerque \textit{et al.} ($2016$), Aron \textit{et al.} ($2017$)…

多重线性型的压缩与解耦不等式与u-统计量

Contraction and decoupling inequalities for multilinear forms and u-statistics

证明了向量空间中系数为独立随机变量的随机多项式的解耦不等式。我们使用各种比较方法，包括重排不变范数（例如，Orlicz和Lorentz范数）、尾部分布、紧密性、超收缩性等。

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。

球拟Banach函数空间相关的Hardy空间上的多重线性算子

Multilinear operators on Hardy spaces associated with ball quasi-Banach function spaces

本文证明了多重线性Calderón--Zygmund算子、极大算子及伪微分算子在球拟Banach函数空间相关的（局部）Hardy空间上有界，结果涵盖多种经典空间，显著推广了现有理论。

稀疏控制蕴含向量值稀疏控制

Sparse domination implies vector-valued sparse domination

本文证明多线性算子的标量值稀疏控制蕴含向量值稀疏控制，引入UMD条件的多线性类比，从而直接获得精确的向量值加权界，并应用于改进Calderón-Zygmund算子与双线性Hilbert变换的界。