Regularity property of some operators on Lipschitz spaces and homogeneous Lipschitz spaces related to biharmonic operator

Triebel-Lizorkin正则性与双Lipschitz映射：复合算子与逆函数正则性

Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity

本文研究双Lipschitz变量替换下Triebel-Lizorkin正则性的稳定性及逆函数正则性，通过给出均匀域上分数光滑Triebel-Lizorkin空间的等价范数（基于末阶弱导数球平均一阶差分）获得结果。

Some remarks on the Lipschitz regularity of Radon transforms

A set in the Euclidean plane is constructed whose image under the classical Radon transform is Lipschitz in every direction. It is also shown that, under mild hypotheses, for any such set the function which maps a direction to the corresponding Lipschitz constant cannot be bounded.

Hilbert transforms along variable planar curves: Lipschitz regularity

In this paper, for $1<p<\infty$, we obtain the $L^p$-boundedness of the Hilbert transform $H^γ$ along a variable plane curve $(t,u(x_1, x_2)γ(t))$, where $u$ is a Lipschitz function with small Lipschitz norm, and $γ$ is a general curve satisfying some suitable smoothness and curvature conditions.

On Lipschitz maps and the Hölder regularity of flows

This paper regroups some of the basic properties of Lipschitz maps and their flows. Many of the results presented here are classical in the case of smooth maps. We prove them here in the Lipschitz case for a better understanding of the Lipschitz geometry and for a quantification of the related properties, which would be of use to the development of numerical methods for rough paths for example. We also introduce the notion of almost Lipschitz maps, which provide a sharper control and description of flows of Lipschitz vector fields and local inverses of Lipschitz injective immersions

一种测度论方法用于Lipschitz正则性及其Haar型小波分析

A measure theoretic approach to Lipschitz regularity and its Haar type wavelet analysis

本文通过广义Haar系统将函数的二进制Lipschitz正则性特征扩展到非原子概率空间，提出新的分析方法。

Convex integration for Lipschitz mappings and counterexamples to regularity

We study Lispchitz solutions of partial differential relations $\nabla u\in K$, where $u$ is a vector-valued function in an open subset of $R^n$. In some cases the set of solutions turns out to be surprisingly large. The general theory is then used to construct counter-examples to regularity of solutions of Euler-Lagrange systems satisfying classical ellipticity conditions.