Journal of Functional Analysis最新文献

英文中文

Ryll-Wojtaszczyk formulas for bihomogeneous polynomials on the sphere 球上双齐次多项式的ryl - wojtaszczyk公式

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-21 DOI: 10.1016/j.jfa.2026.111360

A. Defant , D. Galicer , M. Mansilla , M. Mastyło , S. Muro

We investigate projection constants for spaces of bihomogeneous harmonic and bihomogeneous polynomials on the unit sphere in finite-dimensional complex Hilbert spaces. Using averaging techniques, we demonstrate that the minimal norm projection aligns with the natural orthogonal projection. This result enables us to establish a connection between these constants and weighted

L_{1}

-norms of specific Jacobi polynomials. Consequently, we derive explicit bounds, provide practical expressions for computation, and present asymptotically sharp estimates for these constants. Our findings extend the classical Ryll and Wojtaszczyk formula for the projection constant of homogeneous polynomials in finite-dimensional complex Hilbert spaces to the bihomogeneous setting.

研究了有限维复希尔伯特空间中单位球上双齐次调和多项式和双齐次多项式空间的投影常数。利用平均技术，我们证明了最小范数投影与自然正交投影对齐。这一结果使我们能够建立这些常数与特定雅可比多项式的加权l1范数之间的联系。因此，我们导出了显式边界，提供了实用的计算表达式，并给出了这些常数的渐近尖锐估计。我们的发现将有限维复希尔伯特空间中齐次多项式投影常数的经典Ryll和Wojtaszczyk公式推广到双齐次环境。

引用次数: 0

The convergence and uniqueness of a discrete-time nonlinear Markov chain 离散非线性马尔可夫链的收敛性和唯一性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111367

Ruowei Li , Florentin Münch

In this paper, we prove the convergence and uniqueness of a general discrete-time nonlinear Markov chain with specific conditions. The results have important applications in discrete differential geometry. First, we prove the discrete-time Ollivier Ricci curvature flow

d_{n + 1} ≔ (1 - α κ_{d_{n}}) d_{n}

converges to a constant curvature metric on a finite weighted graph. As shown in [30, Theorem 5.1], a Laplacian separation principle holds on a locally finite graph with nonnegative Ollivier curvature. We further prove that the Laplacian separation flow converges to the constant Laplacian solution and generalizes the result to nonlinear p-Laplace operators. Moreover, our results can also be applied to study the long-time behavior in the nonlinear Dirichlet forms theory and nonlinear Perron-Frobenius theory. Finally, we define the Ollivier Ricci curvature of the nonlinear Markov chain which is consistent with the classical Ollivier Ricci curvature, sectional curvature [5], coarse Ricci curvature on hypergraphs [14] and the modified Ollivier Ricci curvature for p-Laplace. We also establish the convergence results for the nonlinear Markov chain with nonnegative Ollivier Ricci curvature.

本文在特定条件下证明了一类广义离散非线性马尔可夫链的收敛性和唯一性。所得结果在离散微分几何中有重要的应用。首先，证明离散时间Ollivier Ricci曲率流dn+1在有限加权图上收敛于一个常曲率度量。如[30，定理5.1]所示，对于具有非负奥利维尔曲率的局部有限图，拉普拉斯分离原理成立。进一步证明了拉普拉斯分离流收敛于常数拉普拉斯解，并将结果推广到非线性p-拉普拉斯算子。此外，我们的结果也可以应用于非线性Dirichlet形式理论和非线性Perron-Frobenius理论的长时间行为研究。最后，我们定义了非线性马尔可夫链的Ollivier Ricci曲率，该曲率与经典的Ollivier Ricci曲率、截面曲率[5]、超图上的粗Ricci曲率[14]以及p-Laplace下的修正Ollivier Ricci曲率一致。我们还建立了具有非负曲率的非线性马尔可夫链的收敛性结果。

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引用次数: 0

A simple proof of reverse Sobolev inequalities on the sphere and Sobolev trace inequalities on the unit ball 球面上的索博列夫反不等式和单位球上的索博列夫迹不等式的简单证明

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-26 DOI: 10.1016/j.jfa.2026.111380

Runmin Gong , Qiaohua Yang , Shihong Zhang

Frank et al. (2022) [38] stated that there is no relation between the reversed Hardy-Littlewood-Sobolev (HLS) inequalities and reverse Sobolev inequalities. However, we demonstrate that reverse Sobolev inequalities of order

γ \in (\frac{n}{2}, \frac{n}{2} + 1)

on the n-sphere can be readily derived from the reversed HLS inequalities. For the case

γ \in (\frac{n}{2} + 1, \frac{n}{2} + 2)

, we present a simple proof of reverse Sobolev inequalities by using the center of mass condition introduced by Hang. In addition, applying this approach, we establish the quantitative stability of reverse Sobolev inequalities of order

γ \in (\frac{n}{2} + 1, \frac{n}{2} + 2)

with explicit lower bounds. Finally, by using conformally covariant boundary operators and reverse Sobolev inequalities, we derive Sobolev trace inequalities on the unit ball.

Frank et al.(2022)[38]指出，反向Hardy-Littlewood-Sobolev （HLS）不等式与反向Sobolev不等式之间没有关系。然而，我们证明了n球上γ∈(n2,n2+1)阶的反Sobolev不等式可以很容易地由反HLS不等式导出。对于γ∈(n2+1,n2+2)的情况，利用Hang引入的质心条件，给出了逆Sobolev不等式的一个简单证明。此外，利用该方法，我们建立了γ∈(n2+1,n2+2)阶逆Sobolev不等式具有明确下界的定量稳定性。最后，利用共形协变边界算子和逆Sobolev不等式，导出了单位球上的Sobolev迹不等式。

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引用次数: 0

Transition threshold of Couette flow for 2D Boussinesq equations 二维Boussinesq方程的Couette流的过渡阈值

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jfa.2026.111383

Xiaoxia Ren , Dongyi Wei

In this paper, we prove the stability threshold of

\frac{1}{3}

for 2D Boussinesq equations around the Couette flow in

T \times R

with Richardson number

γ^{2} > \frac{1}{4}

and different viscosity ν and thermal diffusivity μ. More precisely, if

{‖ v_{i n} - (y, 0) ‖}_{H^{s + 1 / 2}} + {‖ ρ_{i n} + γ^{2} y - 1 ‖}_{H^{s + 1 / 2}} \leq c {(\min {ν, μ})}^{1 / 3}

\frac{ν + μ}{2 γ \sqrt{ν μ}} < 2 - ε

s > \frac{3}{2}

, then the asymptotic stability holds. This stability threshold is consistent with the optimal stability threshold for the 2D Navier-Stokes equations in Sobolev space. And in the sense of inviscid damping effect, the regularity assumption of the initial data should be sharp.

本文证明了含有理查德森数γ2>；14、不同粘度ν和热扩散系数μ的T×R中Couette流动的二维Boussinesq方程的稳定性阈值为13。更准确地说,如果为vin−(y, 0)为h + 1/2 +为ρy +γ2−1为h + 1/2≤c(最低⁡{ν,μ})1/3,ν+μ2γνμ& lt; 2−ε,s> 32,渐近稳定。该稳定性阈值与Sobolev空间中二维Navier-Stokes方程的最优稳定性阈值一致。在无粘阻尼效应的意义上，初始数据的正则性假设应该是尖锐的。

引用次数: 0

On a class of nonlinear BGK-type kinetic equations with density dependent collision rates 一类具有密度相关碰撞率的非线性bgk型动力学方程

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jfa.2026.111376

Josephine Evans , Daniel Morris , Havva Yoldaş

We consider a class of nonlinear, spatially inhomogeneous kinetic equations of BGK-type with density dependent collision rates. These equations share the same superlinearity as the Boltzmann equation, and fall into the class of run and tumble equations appearing in mathematical biology. We prove that the Cauchy problem is well-posed, and the solutions propagate Maxwellian bounds over time. Moreover, we show that the solutions approach to equilibrium with an exponential rate, known as a hypocoercivity result. Lastly, we derive a class of nonlinear diffusion equations as the hydrodynamic limit of the kinetic equations in the diffusive scaling, employing both hypocoercivity and relative entropy methods. The limit equations cover a wide range of nonlinear diffusion equations including both the porous medium and the fast diffusion equations.

考虑一类具有密度相关碰撞率的非线性空间非齐次bgk型动力学方程。这些方程与玻尔兹曼方程具有相同的超线性，属于数学生物学中出现的奔跑和翻滚方程。我们证明了柯西问题是适定的，并且解随时间传播麦克斯韦界。此外，我们证明了解以指数速率接近平衡，称为准矫顽力结果。最后，利用准矫顽力法和相对熵法，导出了一类非线性扩散方程作为扩散标度中动力学方程的水动力极限。极限方程涵盖了广泛的非线性扩散方程，既包括多孔介质，也包括快速扩散方程。

引用次数: 0

Sharp ℓp inequalities for discrete singular integrals on the lattice Zd 晶格Zd上离散奇异积分的尖锐不等式

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111359

Rodrigo Bañuelos , Daesung Kim , Mateusz Kwaśnicki

This paper investigates higher dimensional versions of the longstanding conjecture verified in [11] that the

ℓ^{p}

-norm of the discrete Hilbert transform on the integers is the same as the

L^{p}

-norm of the Hilbert transform on the real line. It computes the

ℓ^{p}

-norms of a family of discrete operators on the lattice

Z^{d}

d \geq 1

. They are discretizations of a new class of singular integrals on

R^{d}

that have the same kernels as the classical Riesz transforms near zero and similar behavior at infinity. The discrete operators have the same p-norms as the classical Riesz transforms on

R^{d}

. They are constructed as conditional expectations of martingale transforms of Doob h-processes conditioned to exit the upper-half space

R^{d} \times R_{+}

only on the lattice

Z^{d}

. The paper also presents a discrete analogue of the classical method of rotations which gives the norm of a different variant of discrete Riesz transforms on

Z^{d}

. Along the way a new proof is given based on Fourier transform techniques of the key identity used to identify the norm of the discrete Hilbert transform in [11]. Open problems are stated.

本文研究了[11]中证明的长时间猜想的高维版本，即整数上的离散希尔伯特变换的p-范数与实线上的希尔伯特变换的p-范数相同。它计算晶格Zd， d≥1上离散算子族的p-范数。它们是一类新的奇异积分在Rd上的离散化，它们与经典的Riesz变换在零附近有相同的核，在无穷远处有相似的行为。离散算子具有与Rd上的经典Riesz变换相同的p-范数。它们被构造为Doob h过程的鞅变换的条件期望，条件是只能在格Zd上退出上半部空间Rd×R+。本文还给出了经典旋转方法的离散模拟，给出了Zd上离散Riesz变换的不同变体的范数。在此过程中，基于傅里叶变换技术给出了用于识别[11]中离散希尔伯特变换范数的关键恒等式的一个新的证明。说明了尚未解决的问题。

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引用次数: 0

Index estimates for constant mean curvature surfaces in three-manifolds by energy comparison 用能量比较法估计三流形中常平均曲率曲面的指数

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111375

Luca Seemungal, Ben Sharp

We prove a linear upper bound on the Morse index of closed constant mean curvature (CMC) surfaces in orientable three-manifolds in terms of genus, number of branch points and a Willmore-type energy.

利用属、分支点数和willmore型能量证明了可定向三流形中闭常平均曲率曲面的摩尔斯指数的线性上界。

引用次数: 0

Thin spectra for periodic and ergodic word models 周期和遍历词模型的薄谱

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-02-05 DOI: 10.1016/j.jfa.2026.111385

Jake Fillman , Michala N. Gradner , Hannah J. Hendricks

We establish a new and simple criterion that suffices to generate many spectral gaps for periodic word models. This leads to new examples of ergodic Schrödinger operators with Cantor spectra having zero Hausdorff dimension that simultaneously may have arbitrarily small supremum norm together with arbitrarily long runs on which the potential vanishes.

我们建立了一个新的和简单的准则，足以产生许多谱间隙周期词模型。这导致了新的遍历Schrödinger算子的例子，其康托尔谱具有零豪斯多夫维数，同时可能具有任意小的最高范数和任意长的运行，在此运行上势能消失。

引用次数: 0

Large deviation principles for stochastic nonlinear Schrödinger equations driven by Lévy noise l<s:1>杂讯驱动随机非线性Schrödinger方程的大偏差原理

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jfa.2026.111377

Jiahui Zhu , Wei Liu , Jianliang Zhai

In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic nonlinear Schrödinger equation, with either focusing or defocusing nonlinearity, driven by nonlinear multiplicative Lévy noise in the Marcus canonical form. This task is challenging in the current setting due to the presence of the power-type nonlinear term, the lack of regularization effect of the Schrödinger operator and the absence of compactness of embeddings. To overcome these difficulties, we employ a regularization procedure based on Yosida approximations and implement techniques such as time discretization, cut-off arguments, and relative entropy estimates of sequences of probability measures. Our innovative approach circumvents the need for compactness conditions, distinguishing our work from previous studies.

本文建立了具有聚焦或散焦非线性的随机非线性Schrödinger方程的Freidlin-Wentzell型大偏差原理，该方程由Marcus标准形式的非线性乘性lsamvy噪声驱动。由于幂型非线性项的存在、Schrödinger算子的正则化效果的缺乏以及嵌入的紧性的缺乏，这项任务在当前的设置中是具有挑战性的。为了克服这些困难，我们采用了基于Yosida近似的正则化过程，并实现了时间离散化、截止参数和概率测量序列的相对熵估计等技术。我们的创新方法绕过了对紧凑性条件的需求，将我们的工作与以前的研究区分开来。

引用次数: 0

Quantum dynamical bounds for long-range operators with skew-shift potentials 具有斜移势的远程算符的量子动力学界

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jfa.2026.111378

Wencai Liu , Matthew Powell , Xueyin Wang

We employ Weyl's method and Vinogradov's method to analyze skew-shift dynamics on semi-algebraic sets. Consequently, we improve the quantum dynamical upper bounds of Jitomirskaya-Powell, Liu, and Shamis-Sodin for long-range operators with skew-shift potentials.

采用Weyl方法和Vinogradov方法分析了半代数集上的偏移动力学。因此，我们改进了Jitomirskaya-Powell， Liu和Shamis-Sodin对于具有斜移势的远程算子的量子动力学上界。

引用次数: 0

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Journal of Functional Analysis

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