Journal of Functional Analysis最新文献

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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 : 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 : 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

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 : 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 : 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

Boyd indices and the Berger-Coburn phenomenon Boyd指数和Berger-Coburn现象

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-12-08 DOI: 10.1016/j.jfa.2025.111310

Jingbo Xia

We settle the issue of Berger-Coburn phenomenon on the Fock space completely for general symmetrically normed ideals

C_{Φ}

, where Φ is not equivalent to

Φ_{\infty}

. We show that if the Boyd indices of

C_{Φ}

satisfy the condition

1 < p_{Φ} \leq q_{Φ} < \infty

, then for

f \in L^{\infty} (C^{n})

, we have

H_{f} \in C_{Φ}

if and only if

H_{\bar{f}} \in C_{Φ}

. We further show that if either

p_{Φ} = 1

q_{Φ} = \infty

, then there is an

f \in L^{\infty} (C^{n})

such that

H_{f} \in C_{Φ}

while

H_{\bar{f}} \notin C_{Φ}

对于一般对称赋范理想CΦ，我们完全解决了Fock空间上的Berger-Coburn现象问题，其中Φ不等于Φ∞。我们证明了如果CΦ的Boyd指标满足条件1<；pΦ≤qΦ<∞，那么对于f∈L∞(Cn)，当且仅当Hf¯∈CΦ，我们有Hf∈CΦ。进一步证明当pΦ=1或qΦ=∞时，则存在一个f∈L∞(Cn)使得Hf∈CΦ，而Hf¯∈CΦ。

引用次数: 0

Global hypoellipticity for systems in time-periodic Gelfand-Shilov spaces 时间周期Gelfand-Shilov空间中系统的全局亚椭圆性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-12-08 DOI: 10.1016/j.jfa.2025.111300

Fernando de Ávila Silva , Marco Cappiello , Alexandre Kirilov

We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of singular solutions, we fully characterize when the system fails to be globally hypoelliptic.

在时间周期Gelfand-Shilov空间中，研究了一类系数既依赖于时间变量又依赖于空间变量的超定系统的全局亚椭圆性。我们的主要结果提供了这类系统的全局亚椭圆性的充分必要条件，用丢芬蒂恩型估计和系数虚部的变号行为来表述。通过范式化和奇异解的详细构造，充分刻画了系统非全局半椭圆的特征。

引用次数: 0

Integral representations of linear functionals on spaces of holomorphic mappings in the unit ball of Cn 单位球上全纯映射空间上线性泛函的积分表示

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-12-08 DOI: 10.1016/j.jfa.2025.111302

Jerry R. Muir Jr.

We provide an assortment of integral representations of continuous linear functionals on complex and real subspaces of the space

H (B, C^{n})

of holomorphic mappings from the open Euclidean unit ball

B

C^{n}

into

C^{n}

. For complex or real linear functionals ℓ, our main results give representations of the form

ℓ (f) = \int_{K} 〈 f (z), z 〉 d μ (z), ℓ (f) = \int_{K} Re 〈 f (z), z 〉 d μ (z),

respectively, where μ is a complex Borel measure in the complex case or a finite signed or positive Borel measure in the real case,

K \subseteq \overline{B}

is a sphere centered at the origin, and the Hermitian inner product in

C^{n}

is denoted in the integrands. The complex representation broadly applies to closed complex subspaces of

H (B, C^{n})

, while the real versions assume various restrictions on real subspaces of

H (B, C^{n})

whose necessity is explored. Several other representations stem from the main results.

本文给出了从Cn的开欧几里德单位球B到Cn的全纯映射空间H（B,Cn）的复子空间和实子空间上连续线性泛函的一系列积分表示。对于复线性泛函或实线性泛函，我们的主要结果分别给出了形式为∑(f)=∫K < f(z),z > dμ(z),∑(f)=∫KRe < f(z),z > dμ(z)的表示，其中μ在复情况下是复Borel测度，在实情况下是有限符号或正Borel测度，K⊥B是原点为中心的球体，Cn中的hermite内积在积分中表示。复表示广泛适用于H（B,Cn）的闭复子空间，实表示对H（B,Cn）的实子空间进行了各种限制，探讨了其必要性。其他几个表述源于主要结果。

引用次数: 0

Absence of anomalous dissipation for vortex sheets 涡旋片不存在异常耗散

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-12-08 DOI: 10.1016/j.jfa.2025.111304

Tarek M. Elgindi , Milton C. Lopes Filho , Helena J. Nussenzveig Lopes

A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of small viscosity. In this article we present a proof of absence of anomalous dissipation for 2D flows on the torus, with an arbitrary non-negative measure plus an integrable function as initial vorticity and square-integrable initial velocity. Our result applies to flows with forcing and provides an explicit estimate for the dissipation at small viscosity. The proof relies on a new refinement of a classical inequality due to J. Nash.

当不可压缩的Navier-Stokes方程的能量耗散在小黏度的极限下不消失时，其解就会出现反常耗散。本文用一个任意的非负测度加上一个可积函数作为初始涡量和初始速度的平方可积，给出了二维流在环面上不存在异常耗散的证明。我们的结果适用于有强迫的流动，并提供了小粘度下耗散的显式估计。这个证明依赖于纳什对一个经典不等式的新改进。

引用次数: 0

Clustering type solutions for critical elliptic system in dimension two 二维临界椭圆系统的聚类解

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-12-08 DOI: 10.1016/j.jfa.2025.111299

Xu Zhang , Ying Zhang , Rui Zhu

<div><div>We are concerned with clustering-peak solutions to the following stationary Hamiltonian elliptic system<math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><mo>−</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>v</mi><mo>)</mo><mspace></mspace><mspace></mspace><mrow><mtext>in</mtext><mspace></mspace></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo>−</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>v</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mspace></mspace><mspace></mspace><mrow><mtext>in</mtext><mspace></mspace></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mspace></mspace><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>→</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace><mi>v</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>→</mo><mn>0</mn><mspace></mspace><mrow><mi>as</mi></mrow><mspace></mspace><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo><mo>.</mo></mtd></mtr></mtable></mrow></math> Here <math><mi>ε</mi><mo>></mo><mn>0</mn></math> is a small parameter, V has a local maximum point, and <math><mi>f</mi><mo>,</mo><mi>g</mi></math> are assumed to be of critical growth in the sense of the Trudinger–Moser inequality. Differently from most results that consider solutions for the critical equation near the ground state level <math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math>, we attempt to construct high-energy solutions at levels close to <math><mi>k</mi><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math> for any integer k. The solutions possess k peaks that cluster around a local maximum of V as <math><mi>ε</mi><mo>→</mo><mn>0</mn></math>. Due to the critical growth of the nonlinear terms, in order to handle the compactness problem, we make uniform estimates of the exponential integral of functions in a suitable neighborhood. Since there is no non-degeneracy property for the ground state solutions of the limit system, the variational method is applied here, and a sensitive lower gradient estimate should be made when the local centroids of the functions are away from the local maximum of V. We introduce a new method to obtain this estimate, which differs from the ideas of Del Pino and Felmer (2002) [27], and Byeon and Tanaka (2013, 2014) [9], [10]. In addition, the fact that the energy functional corresponding to Hamiltonian elliptic systems is strongly indefinite poses additional difficulties for

我们关注以下平稳哈密顿椭圆系统{−ε2Δu+V(x)u=g(V)inR2,−ε2Δv+V(x) V =f(u)inR2,u(x)→0，V(x)→0as|x|→∞的聚类峰解。这里ε>；0是一个小参数，V有一个局部极大点，f，g在Trudinger-Moser不等式意义上被假定为临界增长。与大多数考虑临界方程在基态能级c0附近的解的结果不同，我们试图在接近kc0的能级上构造任意整数k的高能解。解具有k个峰，这些峰聚集在V的局部最大值ε→0附近。由于非线性项的临界增长，为了处理紧性问题，我们在合适的邻域内对函数的指数积分作了一致估计。由于极限系统的基态解不具有非简并性，本文采用变分方法，当函数的局部质心远离v的局部最大值时，需要进行敏感的低梯度估计。本文引入了一种不同于Del Pino and Felmer(2002)[27]和Byeon and Tanaka(2013, 2014)[9]，[10]的新方法来获得这种估计。此外，哈密顿椭圆系统对应的能量泛函是强不定的，这给我们的证明带来了额外的困难。通过考虑外部区域上的辅助极大极小问题和对初始路径能量的精确估计，得到了该泛函在合适邻域内的连接结构。结合前面提到的梯度估计和应用局部变形的方法，我们得到了系统期望解的存在性。

引用次数: 0

Dimension free estimates for the vector-valued Hardy–Littlewood maximal function on the Heisenberg group Heisenberg群上向量值Hardy-Littlewood极大函数的无维估计

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-11-19 DOI: 10.1016/j.jfa.2025.111285

Pritam Ganguly , Abhishek Ghosh

In this article, we establish dimension-free Fefferman-Stein inequalities for the Hardy-Littlewood maximal function associated with averages over Korányi balls in the Heisenberg group. We also generalize the result to more general UMD lattices. As a key stepping stone, we establish the

L^{p}

- boundedness of the vector-valued Nevo-Thangavelu spherical maximal function, which plays a crucial role in our proofs of the main theorems.

在本文中，我们建立了与海森堡群中Korányi球上的平均值相关的Hardy-Littlewood极大函数的无量纲Fefferman-Stein不等式。我们还将结果推广到更一般的UMD格。作为一个重要的步骤，我们建立了向量值的Nevo-Thangavelu球面极大函数的Lp有界性，它在我们主要定理的证明中起着至关重要的作用。

引用次数: 0

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