Riesz transforms on compact quantum groups and strong solidity

双模系数、Coxeter 群上的 Riesz 变换与强刚性

Bimodule coefficients, Riesz transforms on Coxeter groups and strong solidity

本文利用双模系数的 Schatten 类条件刻画弱包含关系，并研究 Coxeter 群梯度双模，建立 gradient-S_p、紧化小性与奇偶路径的等价性，从而推广强刚性结果。

量子环面与欧几里得空间上以Riesz变换表示的最大Riesz变换

Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space

本文在量子环面和量子欧几里得空间上建立了最大Riesz变换的$L_p$有界性，并证明当$2\leq p<\infty$时范数常数与维数无关。

Riesz-Schur transforms

We investigate nontrigonometric forms of Riesz transforms in the context of Schur multipliers. This refines Grothendieck-Haagerup's endpoint criterion with a new condition for the Schatten p-boundedness of Schur multipliers and strengthens Potapov/Sukochev's solution of Arazy's conjecture. We recover as well dimension-free estimates for trigonometric Riesz transforms. Our discrete approach is much simpler than previous harmonic analysis and probabilistic approaches. As an application, we find a very simple proof of recent criteria for Schur multipliers of Hörmander-Mikhlin and Marcinkiewicz ty…

偏置超立方体上基于非迹婴儿Fock模型的维数无关Riesz变换估计

Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models

本文通过非迹婴儿Fock模型转移，证明偏置超立方体上Riesz变换的维数无关Meyer不等式，并推广至q-Araki--Woods代数。

Noncommutative Riesz transforms -- Dimension free bounds and Fourier multipliers

We obtain dimension free estimates for noncommutative Riesz transforms associated to conditionally negative length functions on group von Neumann algebras. This includes Poisson semigroups, beyond Bakry's results in the commutative setting. Our proof is inspired by Pisier's method and a new Khintchine inequality for crossed products. New estimates include Riesz transforms associated to fractional laplacians in $\mathbb{R}^n$ (where Meyer's conjecture fails) or to the word length of free groups. Lust-Piquard's work for discrete laplacians on LCA groups is also generalized in several ways. In th…

非交换里斯变换--一种概率方法

Noncommutative Riesz transforms -- a probabilistic approach

对于$2\le p<\infty$，我们显示了较低的估计\[ \|A^{\frac 12}x\|_p \kl c(p)\max\{\pl \|Γ(x,x)^{1/2}\|_p,\pl \|Γ(x^*,x^*)^{1/2}\|_p\} \]的里斯变换相关的半群$(T_t)$上的完全正的映射的冯诺依曼代数与负生成元$T_t=e^{-tA}$，和梯度形式\[ 2Γ(x,y)\lel Ax^*y+x^*Ay-A(x^*y)\pl .\]作为额外的假设，我们假设$Γ^2\gl 0$和存在的马尔可夫膨胀$(T_t)$。给出了量子度量空间的应用，并证明了由马氏扩张导出的半群Hardy范数与鞅Hardy范数的等价性。在极限情形下，我们得到了一般完全正映射半群的BMO空间的一个可行定义，它可以作为插值的端点。对于无挠序群，我们构造了由序诱导的里斯变换与希尔伯特变换之间的联系.