Journal of Mathematical Analysis and Applications最新文献

英文中文

Fractional maximal operator in hyperbolic spaces 双曲空间中的分数极大算子

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-22 DOI: 10.1016/j.jmaa.2024.129079

Gonzalo Ibañez-Firnkorn, Emanuel Ramadori

In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study its weighted boundedness. Motivated by the weighted boundedness of the Hardy-Littlewood maximal studied by Antezana and Ombrosi in [1], we give conditions for the weak type and strong type estimate for fractional maximal. Also, we present examples of weights for which the fractional maximal operator satisfies weak type

(p, q)

inequality but strong type

(p, q)

inequality fails.

本文在非加倍测度空间双曲空间上引入分数极大算子，并研究了其加权有界性。利用Antezana和Ombrosi在[1]中研究的Hardy-Littlewood极大值的加权有界性，给出了分数极大值的弱型估计和强型估计的条件。此外，我们还给出了分数极大算子满足弱型（p,q）不等式而强型（p,q）不等式不满足的权重例子。

引用次数: 0

Linear-quadratic stochastic Stackelberg differential games with asymmetric information for systems driven by multi-dimensional jump-diffusion processes 多维跳跃-扩散过程驱动系统的线性-四元随机斯塔克尔伯格微分博弈与非对称信息

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-22 DOI: 10.1016/j.jmaa.2024.129068

Jun Moon

We consider the linear-quadratic stochastic leader-follower Stackelberg differential game for jump-diffusion systems with asymmetric information. In our problem setup, given complete information

F

, leader and follower have access to partial information (filtration)

G_{1} \subset F

and

G_{2} \subset F

, respectively, where

G_{2} \subset G_{1}

captures asymmetric information. Our paper can be viewed as an extension of the complete information (

G_{2} = G_{1} = F

) in [15] to the problem with partial and asymmetric information. By generalizing the stochastic maximum principles and four-step schemes of [15], we obtain the state-feedback representation of the (open-loop type) Stackelberg equilibrium for the leader and the follower in terms of the coupled integro-type Riccati differential equations and the filtering (state) processes with respect to

G_{2}

and

G_{1}

. Indeed, due to the partial and asymmetric information nature, we have to identify new types of the four-step schemes and develop different approaches to obtain the (filtering-based) state-feedback type Stackelberg equilibrium.

我们考虑的是信息不对称的跳跃扩散系统的线性-二次随机领导者-追随者斯塔克尔伯格微分博弈。在我们的问题设置中，在给定完全信息 F 的情况下，领导者和追随者分别可以获得部分信息（过滤）G1⊂F 和 G2⊂F，其中 G2⊂G1 表示信息不对称。我们的论文可以看作是 [15] 中完全信息（G2=G1=F）问题向部分信息和非对称信息问题的扩展。通过推广 [15] 中的随机最大原则和四步方案，我们得到了领导者和追随者的（开环型）斯塔克尔伯格均衡的状态反馈表示，即耦合积分型里卡提微分方程和关于 G2 和 G1 的过滤（状态）过程。事实上，由于信息的片面性和非对称性，我们必须确定四步方案的新类型，并开发不同的方法来获得（基于过滤的）状态反馈型斯泰尔伯格均衡。

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引用次数: 0

Toeplitz operators on Bergman spaces induced by doubling weights in the unit ball of Cn Cn单位球中权加倍诱导Bergman空间上的Toeplitz算子

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-22 DOI: 10.1016/j.jmaa.2024.129077

Juntao Du , Bingyang Hu , Songxiao Li , Xiaojing Zhou

In this paper, we study the boundedness and compactness of the Toeplitz operator

T_{μ} : A_{ω}^{p} \mapsto A_{ω}^{q}

for

1 < p \leq q

, where the weighted Bergman spaces

A_{ω}^{p}

are induced by (radially) doubling weights in the unit ball of

C^{n}

. The equivalence between the boundedness and compactness of

T_{μ} : A_{ω}^{p} \mapsto A_{ω}^{q}

is also established under the assumption with

1 < q < p

. Our work extends the early work of Peláez, Rättyä, and Sierra to higher dimensions, as well as to a larger class of radial weights.

本文研究了1<；p≤q时Toeplitz算子的有界性和紧性，其中加权Bergman空间Aωp是在Cn的单位球上（径向）加倍权引起的。在1<；q<；p的假设下，建立了Tμ:Aωp∈Aωq的有界性与紧性的等价性。我们的工作将Peláez、Rättyä和Sierra的早期工作扩展到更高的维度，以及更大类别的径向权重。

引用次数: 0

A parabolic multiscale inverse problem approached via homogenization: A numerical method 通过均质化解决抛物线多尺度逆问题：数值方法

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-22 DOI: 10.1016/j.jmaa.2024.129073

Vicente Ocqueteau , Raúl Gormaz , Jorge San Martín , Carlos Conca

A method based on homogenization is studied for the solution of a multiscale inverse problem. We consider a class of parabolic problems with highly oscillatory tensors that vary on a microscopic scale. We assume that the microscopic structure is known and seek to recover a macroscopic scalar parameterization of the multiscale tensor. Classical approaches, such as finite elements methods, would require mesh resolution for the direct problem down to the finest scale, that could lead to computational difficulties when implemented. So, starting from the full fine scale model, we solve the inverse problem for a coarse model obtained by homogenization, both theoretically and numerically. The input data, which consist on measurements from the fluxes and the solutions of the direct problem in a given time, are solely based on the original fine scale model. Uniqueness and stability of the inverse problem obtained via homogenization are established under some natural conditions for the fine scale model, and a link with this latter model is established by means of G-convergence. Error estimates are proven for the method.

我们研究了一种基于均质化的多尺度逆问题求解方法。我们考虑了一类具有在微观尺度上变化的高度振荡张量的抛物线问题。我们假设微观结构已知，并寻求恢复多尺度张量的宏观标量参数化。有限元法等经典方法需要将直接问题的网格解析到最细微的尺度，这可能会导致实施时的计算困难。因此，我们从完整的精细尺度模型出发，从理论和数值两方面解决了通过均质化获得的粗模型的逆问题。输入数据包括通量的测量值和给定时间内直接问题的解，完全基于原始的精细模型。在精细尺度模型的一些自然条件下，确定了通过均质化获得的逆问题的唯一性和稳定性，并通过 G 收敛建立了与后一模型的联系。证明了该方法的误差估计值。

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引用次数: 0

Local boundedness for vectorial minimizers of non-uniform variational integrals 非均匀变分积分的向量最小值的局部有界性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-20 DOI: 10.1016/j.jmaa.2024.129074

Zhang Aiping, Feng Zesheng, Gao Hongya

We establish the local boundedness of vectorial local minimizers for a specific class of integral functionals with rank-one convex integrands under appropriate structural assumptions. Our method adapts the renowned De Giorgi‘s iteration technique and employs a suitable Caccioppoli-type inequality. Our findings are applicable to polyconvex integrals

\int_{Ω} {\sum_{α = 1}^{N} λ (x) | D u^{α} |^{p} + μ (x) | D u |^{r}} d x

with suitable

λ (x), μ (x) > 0

and

p, r > 1

我们在适当的结构假设下，为一类具有秩一凸积分的特定积分函数建立了向量局部最小值的局部有界性。我们的方法改编了著名的 De Giorgi 迭代技术，并采用了合适的 Caccioppoli 型不等式。我们的发现适用于具有合适的 λ(x),μ(x)>0 和 p,r>1 的多凸积分∫Ω{∑α=1Nλ(x)|Duα|p+μ(x)|Du|r}dx。

引用次数: 0

Propagation dynamics of the lattice Leslie-Gower predator-prey system in shifting habitats 网格莱斯利-高尔捕食者-猎物系统在变迁生境中的传播动力学

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-20 DOI: 10.1016/j.jmaa.2024.129075

Fei-Ying Yang, Qian Zhao

In this paper, we are concerned with the propagation dynamics of a discrete diffusive Leslie-Gower predator-prey system in shifting habitats. First, we discuss the spreading properties of the corresponding Cauchy problem depending on the range of the shifting speed which is identified respectively by (i) extinction of two species; (ii) only one species surviving; (iii) persistence of two species. Then, we give the existence of two types of forced waves, that is, I type forced waves invading the state where only one species exists in supercritical case and critical case, and II type forced waves invading coexistence state for any speed.

在本文中，我们关注的是一个离散扩散的莱斯利-高尔捕食-猎物系统在移动栖息地中的传播动力学。首先，我们讨论了相应 Cauchy 问题的传播特性，它取决于移动速度的范围，移动速度的范围分别为：(i) 两个物种灭绝；(ii) 只有一个物种存活；(iii) 两个物种持续存在。然后，我们给出了两类强迫波的存在，即在超临界情况和临界情况下入侵只有一种物种存在状态的 I 类强迫波，以及在任意速度下入侵共存状态的 II 类强迫波。

引用次数: 0

Global boundedness in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization 模拟珊瑚受精的二维趋化-纳维尔-斯托克斯系统中的全局有界性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-20 DOI: 10.1016/j.jmaa.2024.129071

Wei Wang, Xi Zhao, Sining Zheng

<div><div>We study the chemotaxis-Navier-Stokes system modeling coral fertilization<span><span><span>(⋆)</span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>n</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>n</mi><mo>=</mo><mi>Δ</mi><mi>n</mi><mo>−</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>n</mi><mi>S</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>c</mi><mo>)</mo><mi>∇</mi><mi>c</mi><mo>)</mo><mo>−</mo><mi>n</mi><mi>m</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>c</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>c</mi><mo>=</mo><mi>Δ</mi><mi>c</mi><mo>−</mo><mi>c</mi><mo>+</mo><mi>m</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>m</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mi>m</mi><mo>=</mo><mi>Δ</mi><mi>m</mi><mo>−</mo><mi>n</mi><mi>m</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>κ</mi><mo>(</mo><mi>u</mi><mo>⋅</mo><mi>∇</mi><mo>)</mo><mi>u</mi><mo>+</mo><mi>∇</mi><mi>P</mi><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mi>∇</mi><mi>ϕ</mi><mo>,</mo><mspace></mspace><mi>∇</mi><mo>⋅</mo><mi>u</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math></span></span></span> in a bounded and smooth domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <span><math><mi>κ</mi><mo>≠</mo><mn>0</mn></math></span>, <span><math><mi>ϕ</mi><mo>∈</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mo>∞</mo></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> and <span><math><mi>S</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>×</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>;</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span> fulfills <span><math><mo>|</mo><mi>S</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>|</mo><mo>≤</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>c</mi><mo>)</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>n</mi><mo>)</mo></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup></math></span> for all <span><math><mo>(</mo><mi>x</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>∈</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>×</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> with <span><math><mi>α</mi><mo>∈</mo><mi>R</mi></math></span> and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>:</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>→</mo><mo>[</mo><mn>0</

我们研究了模拟珊瑚受精的趋化-纳维尔-斯托克斯系统(⋆){nt+u∇⋅n=Δn-∇⋅(nS(x,n,c)∇c)-nm,ct+u⋅∇c=Δc-c+m、mt+u⋅∇m=Δm-nm,ut+κ(u⋅∇)u+∇P=Δu+(n+m)∇j,∇u⋅u=0，在有界光滑域Ω⊂R2 中，其中κ≠0, ϕ∈W2,∞(Ω) 和 S∈C2(Ω¯×[0,∞)2；R2×2) 满足 |S(x,n,c)|≤S0(c)(1+n)-α for all (x,n,c)∈Ω¯×[0,∞)2 with α∈R and S0：[0,∞)→[0,∞)非递减。在之前的工作 W. Wang 等（2021）[22]中，我们已经证明了如果 n|S| 以-12<α<0超线性增长，则相应的（⋆）初边界值问题具有全局解，但不一定是有界解。在本文中，我们将进一步证实这种全局解一定是全局有界的。

引用次数: 0

A strong unique continuation property for weakly coupled elliptic systems 弱耦合椭圆系统的强唯一延续特性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-20 DOI: 10.1016/j.jmaa.2024.129069

Mónica Clapp , Víctor Hernández-Santamaría , Alberto Saldaña

We establish the validity of a strong unique continuation property for weakly coupled elliptic systems, including competitive ones. Our proof exploits the system-structure of the problem and Carleman estimates. Then, we use our unique continuation theorems to show two nonexistence results. The first one states the nonexistence of nontrivial solutions to a weakly coupled elliptic system with a critical nonlinearity and Dirichlet boundary condition on starshaped domains, whereas the second one yields nonexistence of symmetric least energy solutions for a critical system in more general domains.

我们为弱耦合椭圆系统（包括竞争性椭圆系统）建立了强唯一延续性质的有效性。我们的证明利用了问题的系统结构和卡勒曼估计。然后，我们利用唯一续存定理证明了两个不存在结果。第一个结果表明，在星形域中，具有临界非线性和迪里希特边界条件的弱耦合椭圆系统的非微观解不存在，而第二个结果表明，在更一般的域中，临界系统的对称最小能量解不存在。

引用次数: 0

Conjugacy between piecewise monotone functions decreasing on characteristic interval 特征区间上递减的片断单调函数之间的共轭关系

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-19 DOI: 10.1016/j.jmaa.2024.129066

Jialing Zhang , Xiao Tang , Liu Liu

It is known that topological conjugacy is important in the study of functional equations and dynamical systems, since all functions share topological dynamical properties if they are topologically conjugate. In this paper, the necessary and sufficient conditions of topological conjugacy between two piecewise monotone functions of non-monotonicity height 1, which are decreasing on their characteristic intervals, are given.

众所周知，拓扑共轭在函数方程和动力系统的研究中非常重要，因为如果所有函数都是拓扑共轭的，它们就共享拓扑动力特性。本文给出了在特征区间上递减的两个非单调高度为 1 的片断单调函数之间拓扑共轭的必要条件和充分条件。

引用次数: 0

Bivariate generalized Poisson distribution and its relation with 2D–Hermite polynomials 二元广义泊松分布及其与二维赫尔墨特多项式的关系

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2024-11-19 DOI: 10.1016/j.jmaa.2024.129006

Bujar Xh. Fejzullahu

In this paper we consider the bivariate generalized Poisson (G-P) distribution, which is derived from the confluent hypergeometric distribution using the trivariate reduction method. We study some of its important properties such as generating functions, recurrence relations, and differential equations for its probabilities. Furthermore, we show that the certain bivariate G-P distribution is related with the 2D–Hermite type polynomials. As consequence, several formulas for the 2D–Hermite polynomials are obtained.

在本文中，我们考虑了双变量广义泊松（G-P）分布，它是用三变量还原法从汇合超几何分布推导出来的。我们研究了它的一些重要性质，如生成函数、递推关系和概率微分方程。此外，我们还证明了某些双变量 G-P 分布与二维赫尔墨特型多项式相关。因此，我们得到了 2D-Hermite 多项式的几个公式。

引用次数: 0

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