Journal of Functional Analysis最新文献

英文中文

The Klain approach to zonal valuations 克莱恩的区域估值方法

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-11-03 DOI: 10.1016/j.jfa.2025.111249

Leo Brauner , Georg C. Hofstätter , Oscar Ortega-Moreno

We show an analogue of the Klain–Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral representation of zonal valuations involving mixed area measures with a disk. In our argument, we introduce an easy way to translate between this representation and the one involving area measures, yielding a shorter proof of a recent characterization by Knoerr.

As applications, we obtain various integral geometric formulas for

SO (n - 1)

: an additive kinematic, a Kubota-, and a Crofton-type formula. This extends results by Hug, Mussnig, and Ulivelli. Finally, we provide a simpler proof of the integral representation of the mean section operators by Goodey and Weil.

我们展示了一个类似于Klain-Schneider定理的估值，这些估值在绕固定轴旋转时是不变的，称为带状。利用这一点，我们建立了一个新的分区估值的积分表示，涉及混合面积措施与一个磁盘。在我们的论证中，我们引入了一种简单的方法，在这种表示和涉及面积度量的表示之间进行转换，从而产生了对Knoerr最近的表征的更短的证明。作为应用，我们得到了SO（n−1）的各种积分几何公式：一个加性运动学公式，一个Kubota-型公式和一个crofton -型公式。这扩展了Hug、Mussnig和Ulivelli的结果。最后，我们给出了Goodey和Weil对平均截面算子的积分表示的一个更简单的证明。

引用次数: 0

Global hypoellipticity and solvability with loss of derivatives on the torus 环面上导数损失的全局亚椭圆性和可解性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-13 DOI: 10.1016/j.jfa.2025.111231

André Pedroso Kowacs, Alexandre Kirilov

This paper provides a complete characterization of global hypoellipticity and solvability with loss of derivatives for Fourier multiplier operators on the n-dimensional torus. We establish necessary and sufficient conditions for these properties and examine their connections with classical notions of global hypoellipticity and solvability, particularly in relation to the closedness of the operator's range.

As an application, we explore the interplay between these properties and number theory in the context of differential operators on the two-torus. Specifically, we prove that the loss of derivatives in the solvability of the vector field

\partial_{x_{1}} - α \partial_{x_{2}}

is precisely determined by the well-known irrationality measure

μ (α)

of its coefficient α. Furthermore, we analyze the wave operator

\partial_{x_{1}}^{2} - η^{2} Δ_{T^{n}}

and show how the loss of derivatives depends explicitly on the parameter

η > 0

本文给出了n维环面上傅里叶乘子算子的全局亚椭圆性和导数损失可解性的完整刻画。我们建立了这些性质的充分必要条件，并研究了它们与经典的全局半椭圆性和可解性的联系，特别是与算子范围的紧密性的关系。作为一种应用，我们在双环面上的微分算子的背景下探讨了这些性质与数论之间的相互作用。具体来说，我们证明了向量场∂x1−α∂x2的可解性中的导数损失是由其系数α的众所周知的非理性测度μ(α)精确确定的。此外，我们分析了波算子∂x12−η2ΔTn，并展示了导数的损失如何显式地依赖于参数η>；0。

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引用次数: 0

Koebe one-quarter theorem in infinite dimensions 无限维的柯贝四分之一定理

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-10 DOI: 10.1016/j.jfa.2025.111237

Hidetaka Hamada , Gabriela Kohr , Mirela Kohr

In the first part of this paper, we obtain a covering theorem for biholomorphic mappings on bounded domains in a complex Banach space. Next, as an application of this covering theorem, we obtain the Koebe one-quarter theorem for normal Loewner chains on the unit ball of a complex Banach space. We give also several applications of this result. Finally, as another application of the covering theorem obtained in this paper, we obtain a covering theorem for nonlinear resolvents on the unit ball of a complex Banach space.

在本文的第一部分，我们得到了复Banach空间上有界域上生物全纯映射的一个覆盖定理。其次，作为复Banach空间单位球上正规Loewner链的一个应用，得到了复Banach空间单位球上正规Loewner链的Koebe 1 / 4定理。并给出了该结果的几个应用。最后，作为本文所得到的覆盖定理的另一个应用，我们得到了复Banach空间的单位球上非线性解的覆盖定理。

引用次数: 0

Schatten–Lorentz characterization of Riesz transform commutator associated with Bessel operators 与贝塞尔算子相关的Riesz变换换向子的schten - lorentz表征

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-10 DOI: 10.1016/j.jfa.2025.111233

Zhijie Fan , Michael Lacey , Ji Li , Xiao Xiong

Let

Δ_{λ}

be the Bessel operator on the upper half space

R_{+}^{n + 1}

with

n \geq 0

and

λ > 0

, and

R_{λ, j}

be the j-th Bessel Riesz transform,

j = 1, \dots, n + 1

. We demonstrate that the Schatten–Lorentz norm (

S^{p, q}

1 < p < \infty

1 \leq q \leq \infty

) of the commutator

[b, R_{λ, j}]

can be characterized in terms of the oscillation space norm of the symbol b. In particular, for the case

p = q

, the Schatten norm of

[b, R_{λ, j}]

can be further characterized in terms of the Besov norm of the symbol. Moreover, the critical index is also studied, which is

p = n + 1

, the lower dimension of the Bessel measure (but not the upper dimension). Our approach relies on martingale and dyadic analysis, which enables us to bypass the use of Fourier analysis effectively.

设Δλ为上半空间R+n+1上n≥0且λ>；0上的贝塞尔算子，Rλ，j为第j次贝塞尔Riesz变换，j =1，…，n+1。我们证明了换向子[b，Rλ，j]的Schatten - lorentz范数（Sp,q, 1<p<∞,1≤q≤∞）可以用符号b的振荡空间范数来表征，特别是在p=q的情况下，[b,Rλ，j]的Schatten范数可以进一步用符号b的Besov范数来表征。此外，还研究了临界指标p=n+1，即贝塞尔测度的下维（而不是上维）。我们的方法依赖于鞅和二进分析，这使我们能够有效地绕过傅里叶分析的使用。

引用次数: 0

A view from above on JNp(Rn) 俯瞰JNp（Rn）

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-10 DOI: 10.1016/j.jfa.2025.111235

Shahaboddin Shaabani

For a symmetric convex body

K \subset R^{n}

and

1 \leq p < \infty

, we define the space

S^{p} (K)

to be the tent generalization of

{JN}_{p} (R^{n})

, i.e., the space of all continuous functions f on the upper-half space

R_{+}^{n + 1}

such that

{‖ f ‖}_{S^{p} (K)} : = {(\sup_{C} \sum_{B \in C} | f_{B} |^{p})}^{\frac{1}{p}} < \infty,

where, in the above, the supremum is taken over all finite disjoint collections of homothetic copies of K. It is then shown that the dual of

S_{0}^{1} (K)

, the closure of the space of continuous functions with compact support in

S^{1} (K)

, consists of all Radon measures on

R_{+}^{n + 1}

with uniformly bounded total variation on cones with base K and vertex in

R^{n}

. In addition, a similar scale of spaces is defined in the dyadic setting, and for

1 \leq p < \infty

, a complete characterization of their duals is given. We apply our results to study dyadic

{JN}_{p}

spaces.

对称凸体K⊂Rn和1≤术;∞,我们定义的空间Sp (K)的帐篷泛化JNp (Rn),也就是说,所有连续函数f的空间上半空间R + n + 1,为f为Sp (K): = (supC⁡∑B∈C | fB | p) 1术;∞,,在上面的,有限不相交集合的上确界是接管所有类似的副本的双K .然后表明S01 (K),关闭连续函数空间的紧凑支持S1 (K),由R+n+1上所有Radon测度组成，这些Radon测度在以K为底且顶点在Rn上的锥上具有一致有界的总变分。此外，在并矢设置下定义了一个相似的空间尺度，并在1≤p<；∞时，给出了它们对偶的完整表征。我们将所得结果应用于并矢JNp空间的研究。

引用次数: 0

Complemented subspaces of Banach spaces C(K×L) Banach空间C的补子空间（K×L）

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-10 DOI: 10.1016/j.jfa.2025.111236

Grzegorz Plebanek , Jakub Rondoš , Damian Sobota

We prove that, for every compact spaces

K_{1}, K_{2}

and compact group G, if both

K_{1}

and

K_{2}

map continuously onto G, then the Banach space

C (K_{1} \times K_{2})

contains a complemented subspace isometric to the Banach space

C (G)

. Consequently,

C (K_{1} \times K_{2})

contains a complemented copy of

C ([0, 1])

for every non-scattered

K_{1}, K_{2}

. Also, answering a question of Alspach and Galego, we get that

C (β ω \times β ω)

contains a complemented copy of

C ({[0, 1]}^{κ})

for every cardinal number

1 \leq κ \leq c

and hence a complemented copy of

C (K)

for every metric compact space K. On the other hand, for the pointwise topology, we show that

C_{p} (β ω \times β ω)

contains no complemented copy of

C_{p} (2^{ω})

证明了对于每一个紧化空间K1、K2和紧化群G，如果K1和K2连续映射到G上，则巴纳赫空间C（K1×K2）包含一个与巴纳赫空间C(G)等价的补子空间。因此，对于每个非分散的K1，K2， C（K1×K2）包含C（[0,1]）的补充副本。此外，我们还回答了Alspach和Galego的一个问题，得到C（βω×βω）对于每一个1≤κ≤C的基数都包含C（[0,1]κ）的一个补副本，因此对于每一个度量紧化空间K都包含C(K)的一个补副本。另一方面，对于点向拓扑，我们证明了Cp（βω×βω）不包含Cp（2ω）的补副本。

引用次数: 0

Sharp local propagation of chaos for mean field particles with W−1,∞ kernels 具有W−1，∞核的平均场粒子混沌的尖锐局部传播

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-10 DOI: 10.1016/j.jfa.2025.111240

Songbo Wang

We study a system of N diffusive particles with

W^{- 1, \infty}

mean field interaction and establish

O (1 / N^{2})

local propagation of chaos estimates as

N \to \infty

, measured in relative entropy and in weighted

L^{2}

distance. These results extend the work of Lacker (2023) [20] to singular interactions. The entropy bound follows from a hierarchy of relative entropies and Fisher informations, and applies to the 2D viscous vortex model in the weak interaction regime, yielding a uniform-in-time estimate. The

L^{2}

bound is obtained through a hierarchy of

χ^{2}

divergences and Dirichlet energies, leading to sharp short-time estimates for the same model without constraints on the interaction strength.

研究了具有W−1，∞平均场相互作用的N个扩散粒子系统，建立了以相对熵和加权L2距离测量的O（1/N2）局部传播混沌估计为N→∞。这些结果将Lacker(2023)[20]的工作扩展到奇异相互作用。熵界遵循相对熵和Fisher信息的层次结构，并适用于弱相互作用状态下的二维粘性涡模型，从而产生一致的时间估计。L2界是通过χ2散度和Dirichlet能量的层次结构得到的，从而在不受相互作用强度约束的情况下对同一模型进行精确的短时估计。

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引用次数: 0

Exponential mixing by random cellular flows 随机细胞流动的指数混合

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-10 DOI: 10.1016/j.jfa.2025.111227

Víctor Navarro-Fernández , Christian Seis

We study a passive scalar equation on the two-dimensional torus, where the advecting velocity field is given by a cellular flow with a randomly moving centre. We prove that the passive scalar undergoes mixing at a deterministic exponential rate, independent of any underlying diffusivity. Furthermore, we show that the velocity field enhances dissipation and we establish sharp decay rates that, for large times, are deterministic and remain uniform in the diffusivity constant. Our approach is purely Eulerian and relies on a suitable modification of Villani's hypocoercivity method, which incorporates a larger set of Hörmander commutators than Villani's original method.

研究了二维环面上的被动标量方程，其中平流速度场由中心随机移动的元胞流给出。我们证明了被动标量以确定的指数速率进行混合，与任何潜在的扩散率无关。此外，我们证明了速度场增强了耗散，我们建立了急剧的衰减率，在很长一段时间内，这种衰减率是确定的，并且在扩散常数中保持一致。我们的方法是纯粹的欧拉方法，并依赖于维拉尼的准矫顽力方法的适当修改，该方法包含比维拉尼原始方法更大的Hörmander换向子集。

引用次数: 0

On the Kolmogorov equation associated with Volterra equations and fractional Brownian motion 关于与Volterra方程和分数布朗运动相联系的Kolmogorov方程

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-10 DOI: 10.1016/j.jfa.2025.111234

Alessandro Bondi , Franco Flandoli

We consider a Volterra convolution equation in

R^{d}

perturbed with an additive fractional Brownian motion of Riemann–Liouville type with Hurst parameter

H \in (0, 1)

. We show that its solution solves an infinite–dimensional stochastic differential equation (SDE) in the Hilbert space of square–integrable functions. Such an equation motivates our study of an unconventional class of SDEs requiring an original extension of the drift operator and its Fréchet differentials. We prove that these infinite–dimensional SDEs generate a Markov stochastic flow which is twice Fréchet differentiable with respect to the initial data. This stochastic flow is then employed to solve, in the classical sense of infinite–dimensional calculus, the path–dependent Kolmogorov equation corresponding to the SDEs. In particular, we associate a time–dependent infinitesimal generator with the fractional Brownian motion. In the final section, we show some obstructions in the analysis of the mild formulation of the Kolmogorov equation for SDEs driven by the same infinite–dimensional noise. This problem, which is relevant to the theory of regularization by noise, remains open for future research.

考虑具有Hurst参数H∈(0,1)的Riemann-Liouville型加性分数布朗运动摄动的Rd中的Volterra卷积方程。我们证明了它的解在平方可积函数的Hilbert空间中求解一个无限维随机微分方程（SDE）。这样的方程激发了我们对一类非常规的SDEs的研究，这类SDEs需要对漂移算子及其fr微分进行原始扩展。我们证明了这些无限维SDEs生成的马尔可夫随机流相对于初始数据是两次fracimchet可微的。然后利用这个随机流来求解，在经典意义上的无限维微积分中，对应于SDEs的依赖路径的Kolmogorov方程。特别地，我们将一个与时间相关的无穷小发生器与分数布朗运动联系起来。在最后一节中，我们展示了由相同的无限维噪声驱动的SDEs的温和Kolmogorov方程公式分析中的一些障碍。这一问题与噪声正则化理论有关，有待进一步研究。

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引用次数: 0

Quantization and reduction for torsion free CR manifolds 无扭CR流形的量化与约化

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-10-09 DOI: 10.1016/j.jfa.2025.111225

Andrea Galasso , Chin-Yu Hsiao

Consider a compact torsion free CR manifold X and assume that X admits a compact CR Lie group action G. Let L be a G-equivariant rigid CR line bundle over X. It seems natural to consider the space of G-invariant CR sections in the high tensor powers as quantization space, on which a certain weighted G-invariant Fourier–Szegő operator projects. Under certain natural assumptions, we show that the group invariant Fourier–Szegő projector admits a full asymptotic expansion. As an application, if the tensor power of the line bundle is large enough, we prove that quantization commutes with reduction.

考虑一个紧致无挠CR流形X，并假设X存在紧致CR李群作用g。设L是X上的一个g等变刚性CR线束。将高张量幂中g不变CR截面的空间视为量化空间似乎是很自然的，在量化空间上投射着某个加权g不变傅立叶-塞格格算子。在一定的自然假设下，证明了群不变傅里叶-塞格尔投影可以完全渐近展开。作为一个应用，当线束的张量幂足够大时，我们证明了量化与约简相交换。

引用次数: 0

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Journal of Functional Analysis

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