加权Gagliardo-Nirenberg插值不等式

Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schrödinger equation

We study the standing waves for a fourth-order Schrödinger equation with mixed dispersion that minimize the associated energy when the $L^2-$norm (the \textit{mass}) } is kept fixed. We need some non-homogeneous Gagliardo-Nirenberg-type inequalities and we develop a method to prove such estimates that should be useful elsewhere. We prove optimal results on the existence of minimizers in the {\it mass-subcritical } and {\it mass-critical } cases. In the { \it mass supercritical} case we show that global minimizers do not exist, and we investigate the existence of local minimizers. If the mass d…

单射椭圆性、消没算子与向量场的端点Gagliardo-Nirenberg-Sobolev不等式

Injective ellipticity, cancelling operators, and endpoint Gagliardo-Nirenberg-Sobolev inequalities for vector fields

本文通过消没条件刻画使端点Sobolev估计成立的微分算子，统一并推广了Gagliardo-Nirenberg、Korn-Sobolev及Hodge复形等经典不等式，并借助对偶估计与调和分析技术证明，同时引入弱条件刻画$L^\infty$估计。

带应用的精确加权Cohen--Dahmen--Daubechies--DeVore不等式：（加权）临界Sobolev空间、Gagliardo--Nirenberg不等式与Muckenhoupt权

Sharp Weighted Cohen--Dahmen--Daubechies--DeVore Inequality with Applications to (Weighted) Critical Sobolev Spaces, Gagliardo--Nirenberg Inequalities, and Muckenhoupt Weights

本文建立了Cohen等人2003年提出的不等式的精确加权变体，通过发展好立方体方法追踪对A_p权常数的精确依赖，得到加权Sobolev空间刻画、插值及Gagliardo-Nirenberg不等式等应用，还给出了Muckenhoupt权的新刻画并解决了一个公开问题。

Brezis--Van Schaftingen--Yung Formulae in Ball Banach Function Spaces with Applications to Fractional Sobolev and Gagliardo--Nirenberg Inequalities

Let $X$ be a ball Banach function space on ${\mathbb R}^n$. In this article, under some mild assumptions about both $X$ and the boundedness of the Hardy--Littlewood maximal operator on the associate space of the convexification of $X$, the authors prove that, for any locally integrable function $f$ with $\|\,|\nabla f|\,\|_{X}<\infty$, $$\sup_{λ\in(0,\infty)}λ\left \|\left|\left\{y\in{\mathbb R}^n:\ |f(\cdot)-f(y)| >λ|\cdot-y|^{\frac{n}{q}+1}\right\}\right|^{\frac{1}{q}} \right\|_X\sim \|\,|\nabla f|\,\|_X$$ with the positive equivalence constants independent of $f$, where the index $q\in(0,\i…

具有高阶分数阶导数的各向异性Caffarelli-Kohn-Nirenberg不等式

Anisotropic Caffarelli-Kohn-Nirenberg inequalities with higher-order fractional derivatives

证明了一族涉及高阶分数阶导数和形如$|x'|^{\theta_1}|x|^{\theta_2}|x_n|^{\theta_3}$权重的各向异性Caffarelli-Kohn-Nirenberg插值不等式。

一个与Gagliardo和Sobolev半范数相关的尖锐局部加权不等式及其应用

A Sharp Localized Weighted Inequality Related to Gagliardo and Sobolev Seminorms and Its Applications

本文提出一个与Gagliardo和Sobolev半范数相关的近尖锐局部加权不等式，并应用于Muckenhoupt权重的特征以及多个数学不等式的证明。

Improved Caffarelli-Kohn-Nirenberg and trace inequalities for radial functions

We show that Caffarelli-Kohn-Nirenberg first order interpolation inequalities as well as weighted trace inequalities in $\mathbb{R}^n \times \mathbb{R}_+$ admit a better range of power weights if we restrict ourselves to the space of radially symmetric functions.

关于矩阵加权空间中的非对角算子

On off-diagonal operators in matrix-weighted spaces

研究矩阵加权空间中非对角算子，通过凸体控制理论证明分数阶算子及其交换子的矩阵加权不等式，给出相关定量估计及向量值函数的矩阵加权加利亚尔多 - 尼伦伯格 - 索伯列夫不等式。

Caffarelli-Kohn-Nirenberg不等式在弱Lebesgue空间中的应用

Caffarelli-Kohn-Nirenberg Inequalities in Weak Lebesgue Spaces

本文通过调和分析技术推导出在临界参数条件下仍有效的弱型Caffarelli-Kohn-Nirenberg不等式，并获得了在临界维度下成立的弱型Hardy不等式。