Subgaussian Kahane-Salem-Zygmund inequalities in Banach spaces

Constants of the Kahane--Salem--Zygmund inequality asymptotically bounded by $1$ II

In [18] we have shown that, for $p_{1},p_{2}\in(2,\infty]$, the constants of Bennett's inequality on unimodular bilinear forms on $\ell_{p_{1}}^{n_{1} }\times\ell_{p_{2}}^{n_{2}}$ are asymptotically bounded by $1$. In the present paper we use a different approximation technique to investigate the remaining cases $p_{1},p_{2}\in\lbrack1,\infty].$ This new approach also provides a stronger asymptotic control, in the sense that the constants are "uniformly" asymptotically bounded by $1$, with no dependence on $p_{1},p_{2}.$

稀疏Kahane--Salem--Zygmund形式与临界端点处的加权Hardy--Littlewood不等式

Sparse Kahane--Salem--Zygmund Forms and Weighted Hardy--Littlewood Inequalities Across the Critical Endpoint

本文研究稀疏Kahane--Salem--Zygmund构造与加权Hardy--Littlewood不等式，确定了临界端点处最小范数的精确幂次，并引入对角加权泛函，给出最优权重指数及匹配的维数障碍。

希尔伯特空间中的 Kahane--Salem--Zygmund 不等式：极值函数与定量间隙

Hilbertian Kahane--Salem--Zygmund Inequalities: Extremizers and Quantitative Gaps

该研究针对有限维希尔伯特空间上系数为±1的实多重线性型，确定了K_{r,n}=1的条件，推导了等式不成立时的范数间隙，还给出了渐近结果、四阶矩估计及相关构造。

对称 Kahane--Salem--Zygmund 不等式与上确界范数

Symmetric Kahane--Salem--Zygmund Inequalities and the Supremum Norm

本文研究实数域上对称 Kahane--Salem--Zygmund 常数的精确阶，利用 Walsh 谱和 Gram 永久式刚性证明了下界 $\sqrt{2/e}\sqrt{m!}/m$ 与上界 $C_0\sqrt{m!}$，并给出截断 Hadamard 矩阵的矩形估计。

Variants of a multiplier theorem of Kislyakov

We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric polynomials on the $n$-dimensional torus $\mathbb{T}^n$ or Boolean cubes $\{-1,1\}^N$. Our more abstract approach based on local Banach space theory has the advantage that it allows to consider more general compact abelian groups instead of only the multidimensional torus. As an application we show that various recent $\ell_1$-multiplier theorems for trigonome…