Journal of Functional Analysis最新文献

英文中文

On Hermite pseudo–multipliers with non-smooth kernels 非光滑核的Hermite伪乘子

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-01 Epub Date: 2025-12-19 DOI: 10.1016/j.jfa.2025.111323

The Anh Bui , Xuan Thinh Duong , Fu Ken Ly

Let

H

be the Hermite operator on

R^{n}

. For a bounded function

m : R^{n} \times R \to C

, we can define the Hermite pseudo-multipliers

m (x, H)

formally by setting

m (x, H) = \sum_{k = 0}^{\infty} m (x, 2 k + n) P_{k},

where

P_{k}

is the orthogonal projection of

L^{2} (R^{n})

onto the k-th eigenspace of

H

corresponding to the eigenvalue

2 k + n

. In this paper, we consider new conditions on m for which

m (x, H)

may not possess any kernel regularity. For such pseudo-multipliers we establish their boundedness on various function spaces including weighted Lebesgue spaces, BMO and Hardy spaces associated to

H

. In the scale of the weighted Lebesgue spaces, our results improve those in [Bagchi & Thangavelu, J. Funct. Anal. 2015].

设H是Rn上的厄米算子。对于有界函数m:Rn×R→C，我们可以通过设m(x，H)=∑k=0∞m(x,2k+n)Pk来正式定义Hermite伪乘子m(x，H)，其中Pk是L2（Rn）在H的第k个特征空间上对应于特征值2k+n的正交投影。本文考虑m上m（x，H）不具有核正则性的新条件。对于这些伪乘子，我们建立了它们在各种函数空间上的有界性，包括加权Lebesgue空间、BMO和与h相关的Hardy空间。在加权Lebesgue空间的尺度上，我们的结果改进了[Bagchi &； Thangavelu， J. Funct]中的结果。肛交,2015]。

引用次数: 0

Qualitative analysis for ground state solutions of logarithmic Schrödinger equations under a small constant magnetic field in RN 小恒磁场作用下对数Schrödinger方程基态解的定性分析

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-01 Epub Date: 2026-01-06 DOI: 10.1016/j.jfa.2025.111333

Xiaoming An , Shuangjie Peng , Xian Yang , Fulin Zhong

We consider the qualitative properties of ground states of the logarithmic Schrödinger equation with magnetic fields

{(i \nabla + b x^{⊥})}^{2} u = u \log | u | in R^{N},

where

N = 2, 3

, b is a real constant,

x^{⊥} = (- x_{2}, x_{1}, 0)

N = 3

and

(- x_{2}, x_{1})

N = 2

is derived from the magnetic field B in the relation

\nabla \times A = B

. We obtain a ground state solution to the problem by revealing the relation between this equation and the power-law Schrödinger equation

{(i \nabla + b x^{⊥})}^{2} u + u = | u |^{p - 2} u

. For sufficiently small

| b |

, we also demonstrate that the ground state solutions are positive and nondegenerate. Moreover, they are unique and radially symmetric up to magnetic translations and rotations in the complex phase space.

我们考虑对数Schrödinger方程的基态的定性性质，该方程具有磁场（i∇+bx⊥）2u=ulog (|u|inRN，其中N=2,3， b是实常数，如果N=3，则x⊥=(- x2,x1,0)，如果N=2，则（- x2,x1）是从关系∇×A= b中的磁场b推导出来的。通过揭示该方程与幂律Schrödinger方程（i∇+bx⊥）2u+u=|u|p−2u之间的关系，我们获得了该问题的基态解。对于足够小的|b|，我们还证明了基态解是正的和非简并的。此外，它们是唯一的和径向对称的，直到磁平移和旋转在复相空间。

引用次数: 0

On the Meissner state for type-II inhomogeneous superconductors ii型非均匀超导体的迈斯纳态

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-01 Epub Date: 2026-01-06 DOI: 10.1016/j.jfa.2025.111332

Matías Díaz-Vera , Carlos Román

We consider extreme type-II superconductors modeled by the Ginzburg–Landau energy with a pinning term

a_{ε} (x)

, which we assume to be a bounded measurable function such that

b \leq a_{ε} (x) \leq 1

for some constant

b > 0

. A crucial feature of this type of superconductors is the occurrence of vortices, which appear above the so-called first critical field

H_{c_{1}}

. In this paper we estimate this value and characterize the behavior of the Meissner solution, the unique vortexless configuration that globally minimizes the energy below

H_{c_{1}}

. In addition, we show that beyond this value, for applied fields whose strength is slightly below the so-called superheating field

H_{s h}

, there exists a unique Meissner-type solution that locally minimizes the energy.

我们考虑由Ginzburg-Landau能量模型的极端ii型超导体，它具有固定项aε(x)，我们假设它是一个有界的可测量函数，使得b≤aε(x)≤1，对于某常数b>；0。这种超导体的一个关键特征是漩涡的出现，它出现在所谓的第一临界场Hc1之上。在本文中，我们估计了这个值，并描述了迈斯纳解的行为，迈斯纳解是一种独特的无涡构型，它使Hc1以下的能量全局最小。此外，我们表明，在此值之外，对于强度略低于所谓过热场Hsh的应用场，存在唯一的迈斯纳型解，该解在局部使能量最小化。

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引用次数: 0

The σk-Loewner-Nirenberg problem on Riemannian manifolds for k=n2 and beyond k=n2及以上黎曼流形上的σk-Loewner-Nirenberg问题

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-03-15 Epub Date: 2025-12-08 DOI: 10.1016/j.jfa.2025.111306

Jonah A.J. Duncan , Luc Nguyen

<div><div>Let <math><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math> be a smooth compact Riemannian manifold of dimension <math><mi>n</mi><mo>≥</mo><mn>3</mn></math> with smooth non-empty boundary ∂M. Let <math><mi>Γ</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math> be a symmetric convex cone and f a symmetric defining function for Γ satisfying standard assumptions. Denoting by <math><msub><mrow><mi>A</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>u</mi></mrow></msub></mrow></msub></math> the Schouten tensor of a conformal metric <math><msub><mrow><mi>g</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math>, we show that the associated fully nonlinear Loewner-Nirenberg problem<math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>λ</mi><mo>(</mo><mo>−</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mi>u</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>A</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>u</mi></mrow></msub></mrow></msub><mo>)</mo><mo>)</mo><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mspace></mspace><mi>λ</mi><mo>(</mo><mo>−</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mi>u</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>A</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>u</mi></mrow></msub></mrow></msub><mo>)</mo><mo>∈</mo><mi>Γ</mi></mtd><mtd><mtext>on </mtext><mi>M</mi><mo>﹨</mo><mo>∂</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mtext>on </mtext><mo>∂</mo><mi>M</mi></mtd></mtr></mtable></mrow></mrow></math> admits a solution if <math><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>Γ</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>></mo><mn>1</mn><mo>−</mo><mi>δ</mi></math>, where <math><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>Γ</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> is defined by <math><mo>(</mo><mo>−</mo><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>Γ</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>1</mn><mo>)</mo><mo>∈</mo><mo>∂</mo><mi>Γ</mi></math> and <math><mi>δ</mi><mo>></mo><mn>0</mn></math> is a constant depending on certain geometric data. In particular, we solve the <math><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub></math>-Loewner-Nirenberg problem for all <math><mi>k</mi><mo>≤</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math>, which extends recent work of the authors to include the important threshold case <math>

设（Mn,g0）为维数n≥3的光滑紧致黎曼流形，边界为光滑非空∂M。设Γ∧Rn是一个对称凸锥，f是满足标准假设的Γ的一个对称定义函数。用共形度量gu=u−2g0的Schouten张量Agu表示，我们证明了相关的全非线性Loewner-Nirenberg问题{f(λ(−gu−1Agu))=12,λ(−gu−1Agu)∈Γon M∂Mu=0on∂M承认一个解，如果μΓ+>；1−δ δ，其中μΓ+定义为（−μΓ+,1，…，1）∈∂Γ， δ>；0是依赖于某些几何数据的常数。特别地，我们解决了所有k≤n2的σk-Loewner-Nirenberg问题，它扩展了作者最近的工作，包括了k=n2的重要阈值情况。在此过程中，我们建立了具有正边界数据的完全非线性Loewner-Nirenberg问题和相应的Dirichlet边值问题，如果存在一个共形测度g∈[g0]，使得M上λ(−g−1Ag)∈Γ；后两个结果不需要对μΓ+进行假设，并且在（1,0，…，0）∈∂Γ时是新的结果。

引用次数: 0

Small ball probabilities for simple random tensors 简单随机张量的小球概率

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-03-15 Epub Date: 2025-12-08 DOI: 10.1016/j.jfa.2025.111309

Xuehan Hu , Grigoris Paouris

We study the small ball probability of an order-ℓ simple random tensor

X = X^{(1)} \otimes \dots \otimes X^{(ℓ)}

where

X^{(i)}, 1 \leq i \leq ℓ

are independent random vectors in

R^{n}

that are log-concave or have independent coordinates with bounded densities. We show that the probability that the projection of X onto an m-dimensional subspace F falls within a Euclidean ball of length ε is upper bounded by

\frac{ε}{(ℓ - 1)!} {(C \log (\frac{1}{ε}))}^{ℓ}

and also this upper bound is sharp when m is small. We also established that a much better estimate holds true for a random subspace.

我们研究了阶- r简单随机张量X=X(1)⊗⋯⊗X(r)的小球概率，其中X(i)，1≤i≤r是Rn中的独立随机向量，它们是对数凹的或具有具有有界密度的独立坐标。我们证明了X在m维子空间F上的投影落在长度为ε的欧几里得球内的概率的上界为ε(l−1)！（Clog (1ε)），当m很小时，这个上界也很明显。我们还建立了一个更好的估计适用于随机子空间。

引用次数: 0

Estimates of Green and Martin integrals of Schrödinger equations and a semilinear boundary value problem Schrödinger方程的Green和Martin积分的估计及半线性边值问题

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-03-15 Epub Date: 2025-12-17 DOI: 10.1016/j.jfa.2025.111307

Moshe Marcus

Consider Schrödinger operators

L^{V} : = Δ + V

in a bounded Lipschitz domain

Ω \subset R^{N}

. Assume that

V \in C^{1} (Ω)

satisfies

V (x) \leq \bar{a} dist {(x, \partial Ω)}^{- 2}

and a subcriticality condition that guarantees the existence of a ground state

Φ_{V}

. We derive sharp estimates of signed

L_{V}

superharmonic functions that possess an

L_{V}

boundary trace, i.e., a measure boundary trace associated with

L_{V}

. Using these estimates we derive a-priori estimates of positive solutions of a related semilinear boundary value problem.

考虑有界Lipschitz域中的Schrödinger算子LV:=Δ+V Ω∧RN。假设V∈C1（Ω）满足V(x)≤a¯dist（x,∂Ω）−2和保证基态存在的亚临界条件ΦV。我们得到了具有LV边界迹的有符号LV超调和函数的尖锐估计，即与LV相关的测量边界迹。利用这些估计，我们得到了一个相关的半线性边值问题正解的先验估计。

引用次数: 0

Volume preserving spacetime mean curvature flow and foliations of initial data sets 初始数据集的保体积时空平均曲率流和叶理

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-03-15 Epub Date: 2025-12-11 DOI: 10.1016/j.jfa.2025.111313

Jacopo Tenan

We consider volume preserving curvature evolution of surfaces in an asymptotically Euclidean initial data set with positive ADM-energy. The speed is given by a nonlinear function of the mean curvature, which is the spacetime mean curvature recently considered by Cederbaum and Sakovich (2021) [7]. Following a classical approach by Huisken and Yau (1996) [23], we show that the flow starting from suitably round initial surfaces exists for all times and converges to a constant (spacetime) curvature limit. This provides an alternative construction of the STCMC foliation by Cederbaum-Sakovich.

考虑具有正adm能量的渐近欧几里德初始数据集中曲面的保体积曲率演化问题。速度由平均曲率的非线性函数给出，平均曲率是Cederbaum和Sakovich（2021）最近考虑的时空平均曲率。遵循Huisken和Yau(1996)[23]的经典方法，我们证明了从合适的圆形初始表面开始的流在任何时候都存在，并收敛到一个常数（时空）曲率极限。这提供了Cederbaum-Sakovich的STCMC叶理的另一种构造。

引用次数: 0

Endpoint estimates for maximal operators associated to the wave equation 与波动方程相关的最大算子的端点估计

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-03-15 Epub Date: 2025-12-08 DOI: 10.1016/j.jfa.2025.111308

Chu-hee Cho , Sanghyuk Lee , Wenjuan Li

We consider the

H^{s}

–

L^{q}

maximal estimates associated to the wave operator

e^{i t \sqrt{- Δ}} f (x) = \frac{1}{{(2 π)}^{d}} \int_{R^{d}} e^{i (x \cdot ξ + t | ξ |)} \hat{f} (ξ) d ξ .

Rogers–Villarroya proved

H^{s}

–

L^{q}

estimates for the maximal operator f↦

\sup_{t} | e^{i t \sqrt{- Δ}} f |

up to the critical Sobolev exponents

s_{c} (q, d)

. However, the endpoint case estimates for the critical exponent

s = s_{c} (q, d)

have remained open so far. We obtain the endpoint

H^{s_{c} (q, d)}

–

L^{q}

bounds on the maximal operator

f \mapsto \sup_{t} | e^{i t \sqrt{- Δ}} f |

. We also prove that several different forms of the maximal estimates considered by Rogers–Villarroya are basically equivalent to each other.

引用次数: 0

Whittaker functions on GL(4,R) GL（4，R）上的Whittaker函数

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-03-15 Epub Date: 2025-12-08 DOI: 10.1016/j.jfa.2025.111303

Miki Hirano , Taku Ishii , Tadashi Miyazaki

We give explicit formulas of Whittaker functions on

GL (4, R)

for all irreducible generic representations.

给出了GL（4，R）上所有不可约泛型表示的惠特克函数的显式公式。

引用次数: 0

Sharp concentration phenomena in high-dimensional Orlicz balls 高维奥利兹球中的尖锐集中现象

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-03-15 Epub Date: 2025-12-19 DOI: 10.1016/j.jfa.2025.111322

Lorenz Frühwirth, Joscha Prochno

In this article, we present a precise deviation formula for the intersection of two Orlicz balls generated by Orlicz functions V and W. Additionally, we establish a (quantitative) central limit theorem in the critical case and a strong law of large numbers for the “W-norm” of the uniform distribution on

B^{(n, V)}

. Our techniques also enable us to derive a precise formula for the thin-shell concentration of uniformly distributed random vectors in high-dimensional Orlicz balls. In our approach we establish an Edgeworth-expansion using methods from harmonic analysis together with an exponential change of measure argument.

本文给出了由Orlicz函数V和w生成的两个Orlicz球相交的精确偏差公式，并建立了临界情况下的（定量）中心极限定理和B（n，V）上均匀分布的“w -范数”的强大数定律。我们的技术还使我们能够推导出高维Orlicz球中均匀分布的随机向量的薄壳浓度的精确公式。在我们的方法中，我们利用调和分析的方法和测度的指数变化论证建立了一个埃奇沃斯展开式。

引用次数: 0

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