关于欧几里得平面中方向Lipschitz连续性的一则注记

Uniform local Lipschitz continuity of eigenvalues with respect to the potential in $L^1[a,b]$

The present paper shows that the eigenvalue sequence $\{λ_n(q)\}_{n\geqslant 1}$ of regular Sturm-Liouville eigenvalue problem with certain monotonic weights is uniformly Lipschitz continuous with respect to the potential $q$ on any bounded subset of $L^1([a,b],\mathbb{R})$.

Square functions for bi-Lipschitz maps and directional operators

First we prove a Littlewood-Paley diagonalization result for bi-Lipschitz perturbations of the identity map on the real line. This result entails a number of corollaries for the Hilbert transform along lines and monomial curves in the plane. Second, we prove a square function bound for a single scale directional operator. As a corollary we give a new proof of part of a theorem of Katz on direction fields with finitely many directions.

Optimal parameters related with continuity properties of the multilinear fractional integral operator between Lebesgue and Lipschitz spaces

We deal with the boundedness of the multilinear fractional integral operator $I_{γ,m}$ from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces. Our results generalize some previous estimates not only for the linear case but also for the unweighted problem in the multilinear context. We characterize the classes of weights for which the problem described above holds and show the optimal range of the parameters involved. The optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region. We further exhibit examples…

Lipschitz and Fourier type conditions with moduli of continuity in rank 1 symmetric spaces

Sufficient and necessary results have been proven on Lipschitz type integral conditions and bounds of its Fourier transform for an $L^2$ function, in the setting of Riemannian symmetric spaces of rank $1$ whose growth depends on a $k$th-order modulus of continuity.

分支粗糙微分方程解的Lipschitz连续性

The Lipschitz continuity of the solution to branched rough differential equations

本文利用Grossman Larson Hopf代数与张量Hopf代数的同构，将次黎曼几何技术用于分支粗糙微分方程，证明了解对初值、向量场和驱动粗糙路径的显式Lipschitz连续性。

Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^2$ boundedness

We prove the $L^2$ boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.