Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line

关于超过三个范数的柯尔莫哥洛夫型不等式的注记

A note on the Kolmogorov-type inequalities for more than three norms

本文通过标准技术从已知的柯尔莫哥洛夫问题解中获得精确的柯尔莫哥洛夫型不等式，用于估计函数导数的统一范数。

关于电荷的Landau--Kolmogorov型不等式及其应用

On Landau -- Kolmogorov type inequalities for charges and their applications

本文针对绝对连续的电荷证明了锐利的Landau--Kolmogorov型不等式，并解决了Stechkin逼近问题及相关极值问题，应用于Sobolev空间中的本质有界函数。

Agmon-Kolmogorov inequalities on $\ell^2(\Bbb Z^d)$

Landau-Kolmogorov inequalities have been extensively studied on both continuous and discrete domains for an entire century. However, the research is limited to the study of functions and sequences on $\Bbb R$ and $\Bbb Z$, with no equivalent inequalities in higher-dimensional spaces. The aim of this paper is to obtain a new class of discrete Landau-Kolmogorov type inequalities of arbitrary dimension: $$ \|φ\|_{\ell^\infty(\Bbb Z^d)} \leq μ_{p,d}\|\nabla_Dφ\|^{p/2^d}_{\ell^2(\Bbb Z^d)}\, \|φ\|^{1-p/2^d}_{\ell^2(\Bbb Z^d)}, % $$ where the constant $μ_{p,d}$ is explicitly specified. In fact, this…

Log-Sobolev-type inequalities for solutions to stationary Fokker-Planck-Kolmogorov equations

We prove that every probability measure $μ$ satisfying the stationary Fokker-Planck-Kolmogorov equation obtained by a $μ$-integrable perturbation $v$ of the drift term $-x$ of the Ornstein-Uhlenbeck operator is absolutely continuous with respect to the corresponding Gaussian measure $γ$ and for the density $f=dμ/dγ$ the integral of $f |\log (f+1)|^α$ against $γ$ is estimated via $\|v\|_{L^1(μ)}$ for all $α<1/4$, which is a weakened $L^1$-analog of the logarithmic Sobolev inequality. This means that stationary measures of diffusions whose drifts are integrable perturbations of $-x$ are absolute…

多元函数 Sobolev 空间中若干尖锐的 Landau–Kolmogorov–Nagy 型不等式

On some sharp Landau--Kolmogorov--Nagy type inequalities in Sobolev spaces of multivariate functions

本文研究开凸锥上 Sobolev 空间中的尖锐 Landau–Kolmogorov–Nagy 型不等式，并将其推广到电荷导数及多元函数混合导数的范数估计。

Etemadi and Kolmogorov inequalities in noncommutative probability spaces

Based on a maximal inequality type result of Cuculescu, we establish some noncommutative maximal inequalities such as Hajék--Penyi inequality and Etemadi inequality. In addition, we present a noncommutative Kolmogorov type inequality by showing that if $x_1, x_2, \ldots, x_n$ are successively independent self-adjoint random variables in a noncommutative probability space $(\mathfrak{M}, τ)$ such that $τ\left(x_k\right) = 0$ and $s_k s_{k-1} = s_{k-1} s_k$, where $s_k = \sum_{j=1}^k x_j$, then for any $λ> 0$ there exists a projection $e$ such that $$1 - \frac{(λ+ \max_{1 \leq k \leq n} \|x_k\|)…