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Wenhua Wang

Publications and source records attributed to Wenhua Wang.

At least 19 recordsLinked to original sources
arXiv2026

Local Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and Non-negative Self-adjoint Operators on Spaces of Homogeneous Type and Their Applications

Let $(\mathbb X,d,μ)$ be a space of homogeneous type in the sense of Coifman--Weiss, let $X$ be a ball quasi-Banach function space on $\mathbb X$ under suitable maximal-function and associate-space assumptions, and let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb X)$. Assume that, for every $t>0$, the semigroup $e^{-tL}$ admits an integral kernel satisfying a Gaussian upper bound. In this paper, we introduce and systematically study the local Hardy space $h_L^X(\mathbb X)$ associated with $X$ and $L$, defined in terms of a local Lusin area function together with an appropriate low-frequency term. As applications of this theory, we establish the boundedness of the local Riesz transform $\nabla(L+κI)^{-1/2}$ from $h_L^X(\mathbb R^d)$ into the corresponding $X$-valued vector function space for second-order divergence-form elliptic operators. We also obtain a Hörmander-type spectral multiplier theorem for $F(L+I)$ on $h_L^X(\mathbb X)$. Finally, the abstract results are applied to local Orlicz-Hardy spaces, local variable Hardy spaces, and local mixed-norm Hardy spaces. This theory develops Goldberg's original local Hardy space theory [Duke Math. J. {\bf 46} (1979), 27-42; MR0523600] to the setting of ball quasi-Banach function spaces and non-negative self-adjoint operators on spaces of homogeneous type. To the best of our knowledge, several of the results obtained in this paper are new even in the Euclidean setting $\mathbb X:=\mathbb R^d$.

math.FA↗
arXiv2025

Navier-Stokes Equations on Quantum Euclidean Spaces

We investigate in the present paper the Navier-Stokes equations on quantum Euclidean spaces $\mathbb{R}^d_θ$ with $θ$ being a $d\times d$ antisymmetric matrix, which is a standard example of non-compact noncommutative manifolds. The quantum analogues of Ladyzhenskaya and Kato's results are established, that is, we obtain the global well-posedness in the 2D case and the local well-posedness with solution in $L_d(\mathbb{R}^d)$ in higher dimensions. To achieve these optimal results, we develop the related theory of harmonic analysis and function spaces on $\mathbb{R}^d_θ$, and apply the sharp estimates around noncommutative $L_p$-spaces to quantum Navier-Stokes equations. Moreover, our techniques, which are independent of the deformed parameter $θ$, allow us to conclude some results on the semiclassical limits. This is the first instance of systematical applications to the theory of quantum partial differential equations of the powerful real analysis techniques around noncommutative $L_p$-spaces, which date back to the seminal work \cite{PiXu97} in 1997 on noncommutative martingale inequalities. As in classical case, one may expect numerous similar applications in the future.

math.FA↗
arXiv2025

Matrix-Weighted Besov Spaces Associated with Non-isotropic Dilations

Let $α\in\mathbb{R}$, $p\in[1,\infty)$, $q\in(0,\infty]$, $\mathbf{W}$ be a matrix weight, and $A$ be an expansive dilation on $\mathbb{R}^d$. In this paper, the authors firstly investigate and develop some aspects of homogeneous anisotropic Besov spaces $\dot{B}^{α,q}_{p,A}(\mathbb{R}^d,\mathbf{W})$ and inhomogeneous anisotropic Besov spaces $B^{α,q}_{p,A}(\mathbb{R}^d,\mathbf{W})$ theory in the matrix weight setting. Moreover, we show that these spaces are characterized by the magnitude of the $φ$-transforms in appropriate sequence spaces. Notably, all these results remain novel even in the diagonal non-isotropic case (when $A = \mathrm{diag}(λ_1, λ_2, \ldots, λ_d)$ with $\{λ_j\}_{j=1}^d \subset \mathbb{C}$).

math.FA↗
arXiv2025

Estimates for Schrödinger Groups and Imaginary Power Operators on Weak Hardy Spaces Associated with Non-negative Self-adjoint Operators and Ball Quasi-Banach Function Spaces

Let $(\mathbb{X},d,μ)$ be a doubling metric measure space, $L$ a non-negative self-adjoint operator on $L^2(\mathbb{X})$ satisfying the Davies-Gaffney estimate, and $X(\mathbb{X})$ a ball quasi-Banach function space on $\mathbb{X}$ satisfying some mild assumptions with $p\in(0,\infty)$ and $s_0\in(0,\min\{p,1\}]$. In this article, the authors study the weak Hardy space $WH_{X,L}(\mathbb{X})$ associated with $L$ and $X(\mathbb{X})$, and then give the atomic and molecular decompositions of $WH_{X,L}(\mathbb{X})$. As applications, the authors establish the boundedness estimate of Schrödinger groups for fractional powers of $L$ on $WH_{X,L}(\mathbb{X})$: $$\left\|(I+L)^{-β/2}e^{iτL^{γ/2}}f\right\|_{WH_{X,L}(\mathbb{X})}\leq C\left(1+|τ|\right)^{n(\frac{1}{s_0}-\frac{r}{2})}\|f\|_{WH_{X,L}(\mathbb{X})},$$ where $0<γ\neq1$, $β\in[γn(\frac{1}{s_0}-\frac{1}{2}),\infty)$, $r\in(0,1]$, $τ\in \mathbb{R}$, and $C>0$ is a constant. Moreover, when $(\mathbb{X},d,μ)$ is an Ahlfors $n$-regular metric measure space and $L$ satisfies the Gaussian upper bound estimate, the authors also obtain the boundedness estimate of imaginary power operators of $L$ on $WH_{X,L}(\mathbb{X})$: $$\left\|L^{iτ}f\right\|_{WH_{X,L}(\mathbb{X})}\leq C\left(1+|τ|\right)^{n(\frac{1}{s_0}-\frac{r}{2})}\|f\|_{WH_{X,L}(\mathbb{X})},$$ where $α>n(\frac{1}{s_0}-\frac{1}{2})$, $r\in(\frac{n/s_0}{α+n/2},1]$, $τ\in \mathbb{R}$, and $C>0$ is a constant. These results are also novelty for strong Hardy spaces $H_{X,L}(\mathbb{X})$. Moreover, all these results have a wide range of generality and, particularly, even when they are applied to weighted Lebesgue spaces, mixed-norm Lebesgue spaces, Orlicz spaces, variable Lebesgue spaces and Euclidean spaces setting, these results are also new.

math.CA↗
arXiv2025

Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let $X$ be a ball quasi-Banach function space, $α\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, which is defined via the non-tangential grand maximal function. Under some mild assumptions on $X$, the authors establish the atomic decompositions of $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$. As an application, the authors obtain the boundedness of certain sublinear operators from $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ to $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, where $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ denotes the Herz-type space associated with ball quasi-Banach function space $X$. Finally, the authors apply these results to three concrete function spaces: Herz-type Hardy spaces with variable exponent, mixed Herz-Hardy spaces and Orlicz-Herz Hardy spaces, which belong to the family of Herz-type Hardy spaces associated with ball quasi-Banach function spaces.

math.FA↗
arXiv2025

Real-variable Theory of Anisotropic Musielak-Orlicz-Lorentz Hardy Spaces with Applications to Calderón-Zygmund Operators

Let $φ: \mathbb{R}^{n}\times[0,\infty)\rightarrow[0,\infty)$ be a Musielak-Orlicz function satisfying the uniformly anisotropic Muckenhoupt condition and be of uniformly lower type $p^-_φ$ and of uniformly upper type $p^+_φ$ with $0<p^-_φ\leq p^+_φ<\infty$, $q\in(0,\infty]$, and $A$ be a general expansive matrix on $\mathbb{R}^{n}$. In this article, the authors first introduce the anisotropic Musielak-Orlicz-Lorentz Hardy space $H^{φ,q}_A(\mathbb{R}^{n})$ which, when $q=\infty$, coincides with the known anisotropic weak Musielak-Orlicz Hardy space $H^{φ,\infty}_A(\mathbb{R}^{n})$, and then establish atomic and molecular characterizations of $H^{φ,q}_A(\mathbb{R}^{n})$. As applications, the authors prove the boundedness of anisotropic Calderón-Zygmund operators on $H^{φ,q}_A(\mathbb{R}^{n})$ when $q\in(0,\infty)$ or from the anisotropic Musielak-Orlicz Hardy space $H^φ_A(\mathbb{R}^{n})$ to $H^{φ,\infty}_A(\mathbb{R}^{n})$ in the critical case. The ranges of all the exponents under consideration are the best possible admissible ones which particularly improve all the known corresponding results for $H^{φ,\infty}_A(\mathbb{R}^{n})$ via widening the original assumption $0<p^-_φ\leq p^+_φ\leq1$ into the full range $0<p^-_φ\leq p^+_φ<\infty$, and all the results when $q\in(0,\infty)$ are new and generalized from isotropic setting to anisotropic setting.

math.CA↗
arXiv2025

LL-Localizer: A Life-Long Localization System based on Dynamic i-Octree

This paper proposes an incremental voxel-based life-long localization method, LL-Localizer, which enables robots to localize robustly and accurately in multi-session mode using prior maps. Meanwhile, considering that it is difficult to be aware of changes in the environment in the prior map and robots may traverse between mapped and unmapped areas during actual operation, we will update the map when needed according to the established strategies through incremental voxel map. Besides, to ensure high performance in real-time and facilitate our map management, we utilize Dynamic i-Octree, an efficient organization of 3D points based on Dynamic Octree to load local map and update the map during the robot's operation. The experiments show that our system can perform stable and accurate localization comparable to state-of-the-art LIO systems. And even if the environment in the prior map changes or the robots traverse between mapped and unmapped areas, our system can still maintain robust and accurate localization without any distinction. Our demo can be found on Blibili (https://www.bilibili.com/video/BV1faZHYCEkZ) and youtube (https://youtu.be/UWn7RCb9kA8) and the program will be available at https://github.com/M-Evanovic/LL-Localizer.

cs.RO↗
arXiv2024

Optimizing Age of Information in Vehicular Edge Computing with Federated Graph Neural Network Multi-Agent Reinforcement Learning

With the rapid development of intelligent vehicles and Intelligent Transport Systems (ITS), the sensors such as cameras and LiDAR installed on intelligent vehicles provides higher capacity of executing computation-intensive and delay-sensitive tasks, thereby raising deployment costs. To address this issue, Vehicular Edge Computing (VEC) has been proposed to process data through Road Side Units (RSUs) to support real-time applications. This paper focuses on the Age of Information (AoI) as a key metric for data freshness and explores task offloading issues for vehicles under RSU communication resource constraints. We adopt a Multi-agent Deep Reinforcement Learning (MADRL) approach, allowing vehicles to autonomously make optimal data offloading decisions. However, MADRL poses risks of vehicle information leakage during communication learning and centralized training. To mitigate this, we employ a Federated Learning (FL) framework that shares model parameters instead of raw data to protect the privacy of vehicle users. Building on this, we propose an innovative distributed federated learning framework combining Graph Neural Networks (GNN), named Federated Graph Neural Network Multi-Agent Reinforcement Learning (FGNN-MADRL), to optimize AoI across the system. For the first time, road scenarios are constructed as graph data structures, and a GNN-based federated learning framework is proposed, effectively combining distributed and centralized federated aggregation. Furthermore, we propose a new MADRL algorithm that simplifies decision making and enhances offloading efficiency, further reducing the decision complexity. Simulation results demonstrate the superiority of our proposed approach to other methods through simulations.

cs.LG↗
arXiv2024

Cooperative Edge Caching Based on Elastic Federated and Multi-Agent Deep Reinforcement Learning in Next-Generation Network

Edge caching is a promising solution for next-generation networks by empowering caching units in small-cell base stations (SBSs), which allows user equipments (UEs) to fetch users' requested contents that have been pre-cached in SBSs. It is crucial for SBSs to predict accurate popular contents through learning while protecting users' personal information. Traditional federated learning (FL) can protect users' privacy but the data discrepancies among UEs can lead to a degradation in model quality. Therefore, it is necessary to train personalized local models for each UE to predict popular contents accurately. In addition, the cached contents can be shared among adjacent SBSs in next-generation networks, thus caching predicted popular contents in different SBSs may affect the cost to fetch contents. Hence, it is critical to determine where the popular contents are cached cooperatively. To address these issues, we propose a cooperative edge caching scheme based on elastic federated and multi-agent deep reinforcement learning (CEFMR) to optimize the cost in the network. We first propose an elastic FL algorithm to train the personalized model for each UE, where adversarial autoencoder (AAE) model is adopted for training to improve the prediction accuracy, then {a popular} content prediction algorithm is proposed to predict the popular contents for each SBS based on the trained AAE model. Finally, we propose a multi-agent deep reinforcement learning (MADRL) based algorithm to decide where the predicted popular contents are collaboratively cached among SBSs. Our experimental results demonstrate the superiority of our proposed scheme to existing baseline caching schemes.

cs.LG↗
arXiv2023

URLLC-Awared Resource Allocation for Heterogeneous Vehicular Edge Computing

Vehicular edge computing (VEC) is a promising technology to support real-time vehicular applications, where vehicles offload intensive computation tasks to the nearby VEC server for processing. However, the traditional VEC that relies on single communication technology cannot well meet the communication requirement for task offloading, thus the heterogeneous VEC integrating the advantages of dedicated short-range communications (DSRC), millimeter-wave (mmWave) and cellular-based vehicle to infrastructure (C-V2I) is introduced to enhance the communication capacity. The communication resource allocation and computation resource allocation may significantly impact on the ultra-reliable low-latency communication (URLLC) performance and the VEC system utility, in this case, how to do the resource allocations is becoming necessary. In this paper, we consider a heterogeneous VEC with multiple communication technologies and various types of tasks, and propose an effective resource allocation policy to minimize the system utility while satisfying the URLLC requirement. We first formulate an optimization problem to minimize the system utility under the URLLC constraint which modeled by the moment generating function (MGF)-based stochastic network calculus (SNC), then we present a Lyapunov-guided deep reinforcement learning (DRL) method to convert and solve the optimization problem. Extensive simulation experiments illustrate that the proposed resource allocation approach is effective.

eess.SP↗
arXiv2023

Operator-Valued Hardy spaces and BMO Spaces on Spaces of Homogeneous Type

Let $\mathcal{M}$ be a von Neumann algebra equipped with a normal semifinite faithful trace, $(\mathbb{X},\,d,\,μ)$ be a space of homogeneous type in the sense of Coifman and Weiss, and $\mathcal{N}=L_\infty(\mathbb{X})\overline{\otimes}\mathcal{M}$. In this paper, we introduce and then conduct a systematic study on the operator-valued Hardy space $\mathcal{H}_p(\mathbb{X},\,\mathcal{M})$ for all $1\leq p<\infty$ and operator-valued BMO space $\mathcal{BMO}(\mathbb{X},\,\mathcal{M})$. The main results of this paper include $H_1$--$BMO$ duality theorem, atomic decomposition of $\mathcal{H}_1(\mathbb{X},\,\mathcal{M})$, interpolation between these Hardy spaces and BMO spaces, and equivalence between mixture Hardy spaces and $L_p$-spaces. %Compared with the communcative results, the novelty of this article is that $μ$ is not assumed to satisfy the reverse double condition. %The approaches we develop bypass the use of harmonicity of infinitesimal generator, which allows us to extend Mei's seminal work \cite{m07} to a broader setting. %Our results extend Mei's seminal work \cite{m07} to a broader setting. In particular, without the use of non-commutative martingale theory as in Mei's seminal work \cite{m07}, we provide a direct proof for the interpolation theory. Moreover, under our assumption on Calderón representation formula, these results are even new when going back to the commutative setting for spaces of homogeneous type which fails to satisfy reverse doubling condition. As an application, we obtain the $L_p(\mathcal{N})$-boundedness of operator-valued Calderón-Zygmund operators.

math.FA↗
arXiv2023

Joint Task Scheduling and Container Image Caching in Edge Computing

In Edge Computing (EC), containers have been increasingly used to deploy applications to provide mobile users services. Each container must run based on a container image file that exists locally. However, it has been conspicuously neglected by existing work that effective task scheduling combined with dynamic container image caching is a promising way to reduce the container image download time with the limited bandwidth resource of edge nodes. To fill in such gaps, in this paper, we propose novel joint Task Scheduling and Image Caching (TSIC) algorithms, specifically: 1) We consider the joint task scheduling and image caching problem and formulate it as a Markov Decision Process (MDP), taking the communication delay, waiting delay, and computation delay into consideration; 2) To solve the MDP problem, a TSIC algorithm based on deep reinforcement learning is proposed with the customized state and action spaces and combined with an adaptive caching update algorithm. 3) A real container system is implemented to validate our algorithms. The experiments show that our strategy outperforms the existing baseline approaches by 23\% and 35\% on average in terms of total delay and waiting delay, respectively.

cs.DC↗
arXiv2022

Asynchronous Federated Learning Based Mobility-aware Caching in Vehicular Edge Computing

Vehicular edge computing (VEC) is a promising technology to support real-time applications through caching the contents in the roadside units (RSUs), thus vehicles can fetch the contents requested by vehicular users (VUs) from the RSU within short time. The capacity of the RSU is limited and the contents requested by VUs change frequently due to the high-mobility characteristics of vehicles, thus it is essential to predict the most popular contents and cache them in the RSU in advance. The RSU can train model based on the VUs' data to effectively predict the popular contents. However, VUs are often reluctant to share their data with others due to the personal privacy. Federated learning (FL) allows each vehicle to train the local model based on VUs' data, and upload the local model to the RSU instead of data to update the global model, and thus VUs' privacy information can be protected. The traditional synchronous FL must wait all vehicles to complete training and upload their local models for global model updating, which would cause a long time to train global model. The asynchronous FL updates the global model in time once a vehicle's local model is received. However, the vehicles with different staying time have different impacts to achieve the accurate global model. In this paper, we consider the vehicle mobility and propose an Asynchronous FL based Mobility-aware Edge Caching (AFMC) scheme to obtain an accurate global model, and then propose an algorithm to predict the popular contents based on the global model. Experimental results show that AFMC outperforms other baseline caching schemes.

cs.DC↗
arXiv2022

The Fourier Transform of Anisotropic Hardy Spaces with Variable Exponents and Their Applications

Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-Hölder continuous condition. Let $\mathcal{H}^{p(\cdot)}_A({\mathbb {R}}^n)$ be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the authors obtain that the Fourier transform of $f\in \mathcal{H}^{p(\cdot)}_A({\mathbb {R}}^n)$ coincides with a continuous function $F$ on $\mathbb{R}^n$ in the sense of tempered distributions. As applications, the authors further conclude a higher order convergence of the continuous function $F$ at the origin and then give a variant of the Hardy-Littlewood inequality in the setting of anisotropic Hardy spaces with variable exponents.

math.CA↗
arXiv2022

The Characterizations of Anisotropic Mixed-Norm Hardy Spaces on $\mathbb{R}^n$ by Atoms and Molecules

Let $\vec{p}\in(0,\,\infty)^n$, $A$ be an expansive dilation on $\mathbb{R}^n$,and $H^{\vec{p}}_A({\mathbb {R}}^n)$ be the anisotropic mixed-norm Hardy space defined via the non-tangential grand maximal function studied by \cite{hlyy20}. In this paper, the authors establish new atomic and molecular decompositions of $H^{\vec{p}}_A({\mathbb {R}}^n)$. As an application, the authors obtain a boundedness criterion for a class of linear operators from $H^{\vec{p}}_{A}(\mathbb{R}^n)$ to $H^{\vec{p}}_{A}(\mathbb{R}^n)$. Part of results are still new even in the classical isotropic setting (in the case $A:=2\mathrm I_{n\times n}$, ${\mathrm{I}}_{n\times n}$ denotes the $n\times n$ unit matrix).

math.FA↗
arXiv2021

Maximal Function Characterizations of Hardy Spaces on ${\mathbb{R}}^{n}$ with Pointwise Variable Anisotropy

In 2011, Dekel et al. developed highly geometric Hardy spaces $H^p(Θ)$, for the full range $0<p\leq 1$, which are constructed by continuous multi-level ellipsoid covers $Θ$ of $\mathbb{R}^n$ with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level. In this article, if the cover $Θ$ is pointwise continuous, then the authors further obtain some real-variable characterizations of $H^p(Θ)$ in terms of the radial, the non-tangential and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaces of Bownik.

math.FA↗