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Yongsheng Han

Publications and source records attributed to Yongsheng Han.

At least 19 recordsLinked to original sources
arXiv2026

A Fefferman--Stein inequality for the Dunkl Poisson semigroup and its chamber-lifted formulation

We prove a Fefferman--Stein good-$\lambda$ inequality for the Dunkl Poisson semigroup associated with a finite reflection group and a non-negative multiplicity function. For arbitrary complex-valued $f\in C_c^\infty(\mathbb R^N)$, with no $G$-invariance assumption, it compares the orbit-conical non-tangential maximal function $\mathcal N_P^\beta f$ with the area function $\mathcal S_Pf$ formed from the full space-time Dunkl carr\'e du champ, including its reflection-difference energy. The main obstruction is that a general cut-off creates wall differences not controlled by the local Euclidean-gradient product identity. The good set $E=\{x:\mathcal N_P^\beta f(x)\le\lambda\}$ is $G$-invariant; by the equivariance of the Poisson semigroup, so is $a=\varphi(P_t \mathbf 1_E)$, and hence all reflection differences of the cut-off vanish. Poisson maximal and tail estimates, together with the $L^2$ Littlewood--Paley estimate for $P_t \mathbf 1_{E^c}$, then yield the desired distribution inequality. Its integrated form gives maximal-to-area estimates for every $0<p<2$ and endpoint $H^1$-to-$L^1$ bounds for the orbit-conical and Euclidean-conical intrinsic area functions. For chamber lifts of globally smooth data, the inequality has an equivalent formulation on a fundamental chamber, where orbit cones become Euclidean cones and the reflection energy becomes a finite wall coupling. Combined with the known semigroup square-function characterization, these bounds characterize the Dunkl Poisson maximal Hardy space among $L^1(d\omega)$ data.

math.CA↗
arXiv2026

On the parabolic $H^p$ theory generated by $(p,\infty)$-atoms for $0<p<1$

We study the parabolic maximal operator $M_{\textrm{par}}$ along the moment curve $(t,t^2)$. In 1988, Christ proved that $M_{\textrm{par}}$ maps the parabolic Hardy space $H_{\textrm{par}}^1(\mathbb R^2)$, formulated using $(1,\infty)$-atoms, into $L^{1,\infty}(\mathbb R^2)$. Working directly with parabolic $(p,\infty)$-atoms, we show that this result is sharp at $p=1$: for every $0<p<1$, the natural extension from $H_{\textrm{par}}^p(\mathbb R^2)$ to $L^{p,\infty}(\mathbb R^2)$ fails even for the corresponding single-scale operator. We then introduce a curvature-adapted modified Hardy space $H_{\textrm{par}}^{p,*}(\mathbb R^2)$ and a weak tendril space $\mathcal T^{p,\infty}(\mathbb R^2)$, and prove that $$ M_{\textrm{par}}: H_{\textrm{par}}^{p,*}(\mathbb R^2) \longrightarrow \mathcal T^{p,\infty}(\mathbb R^2), \qquad 0<p<1, $$ is bounded. At $p=1$, these spaces recover those in Christ's theorem: $H_{\textrm{par}}^{1,*}(\mathbb R^2)=H_{\textrm{par}}^1(\mathbb R^2)$ and $\mathcal T^{1,\infty}(\mathbb R^2)=L^{1,\infty}(\mathbb R^2)$. Thus, our result provides a natural extension of Christ's work to the range $0<p<1$.

math.CA↗
arXiv2026

Scalable Conformal MoSx Catalyst for Efficient Hydrogen Evolution at Industrial-Level Current Density in Alkaline Electrolyzers

The development of simple and scalable fabrication strategies for cost-effective electrodes is crucial to advance water splitting in alkaline water electrolyzers (AWEs). Here, we present a coating-annealing method to conformally coat a MoSx catalyst layer onto a porous Ni foam (NF) substrate. By controlling the annealing process, the composition of the MoSx layer could be tuned from MoS2 to MoS3 and its catalytic performance for hydrogen evolution reaction (HER) in alkaline media was optimized. The MoS3@NF synthesized by this method achieved industrially relevant HER current densities of 200 mA/cm2 at a low overpotential of 246 mV, maintaining stable operation for over 240 h. The MoS3@NF cathode, combined with a stainless steel anode, enabled an alkaline water electrolyzer (AWE) cell to operate steadily at 1.96 V and 1 A/cm2 for 1000 h. This performance surpasses that of most of the previously reported water electrolyzers employing MoSx-based cathodes. Our work demonstrates the potential of MoS3 (with its abundant edge-sulfur atoms serving as active sites) as a high-performance cathode material for industrial AWEs.

cond-mat.mtrl-sci↗
arXiv2026

Calderon-type commutators and chamber lifting in the Dunkl setting

Let $G$ be a finite reflection group, and let $T_j$, $\Delta_\kappa$, and $d\omega$ denote its Dunkl operators, Laplacian, and measure, respectively. Write $\mathcal R_j=-T_j(-\Delta_\kappa)^{-1/2}$ for the $j$th Dunkl Riesz transform. We study the Calder\'on-type commutator $[M_b,T_i\mathcal R_j]$ on the full space $L^p(\R^N,d\omega)$, without assuming $G$-invariance of the functions. For $b\in\Lipd$, a full-space Dunkl $T1$ argument for $[M_b,(-\Delta_\kappa)^{1/2}]$, combined with the exact factorization $$ [M_b,T_i\mathcal R_j] =-M_{\partial_i b}\mathcal R_j-\mathcal R_iM_{\partial_jb} +\mathcal R_i[M_b,(-\Delta_\kappa)^{1/2}]\mathcal R_j, $$ implies boundedness on $L^p(d\omega)$ for every $1<p<\infty$. We also prove that the prescribed heat truncations are uniformly bounded on $L^2(d\omega)$ and converge jointly to this operator. To control these truncations, we lift all reflected values of an arbitrary function to separate coordinates on a fixed Weyl chamber. This chamber lifting retains all non-$G$-invariant information and places every possible orbit singularity on the ordinary chamber diagonal of a finite matrix operator. Wall-layer estimates and scalar $T1$ bounds for the integrated entries are uniform in both heat endpoints. A dense-core argument then proves joint, path-independent weak-operator convergence to the factorized commutator. The lifted limit is associated, in the separated-support sense, with a finite matrix of scalar Calder\'on--Zygmund kernels on the chamber.

math.CA↗
arXiv2026

A Covariance Matching Approach to Graph Topology Identification

Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models or complex optimization formulations, commonly suffering from non-convexity or requiring restrictive assumptions on acyclicity or positivity. In this paper, we propose a novel covariance matching (CovMatch) framework that directly aligns the empirical covariance of the observed data with the theoretical covariance implied by an underlying graph. We show that as long as the data-generating process permits an explicit covariance expression, CovMatch offers a unified route to topology inference. We showcase our methodology on linear structural equation models (SEMs), showing that CovMatch naturally handles both undirected and general sparse directed graphs - whether acyclic or positively weighted - without explicit knowledge of these structural constraints. Through appropriate reparameterizations, CovMatch simplifies the graph learning problem to either a conic mixed integer program for undirected graphs or an orthogonal matrix optimization for directed graphs. Numerical results confirm that, even for relatively large graphs, our approach efficiently recovers the true topology and outperforms standard baselines in accuracy. These findings highlight CovMatch as a powerful alternative to log-determinant or Bayesian methods for GTI, paving the way for broader research on learning complex network topologies with minimal assumptions.

eess.SP↗
arXiv2025

Orderbook Feature Learning and Asymmetric Generalization in Intraday Electricity Markets

Accurate probabilistic forecasting of intraday electricity prices is critical for market participants to inform trading decisions. Existing studies rely on specific domain features, such as Volume-Weighted Average Price (VWAP) and the last price. However, the rich information in the orderbook remains underexplored. Furthermore, these approaches are often developed within a single country and product type, making it unclear whether the approaches are generalizable. In this paper, we extract 384 features from the orderbook and identify a set of powerful features via feature selection. Based on selected features, we present a comprehensive benchmark using classical statistical models, tree-based ensembles, and deep learning models across two countries (Germany and Austria) and two product types (60-min and 15-min). We further perform a systematic generalization study across countries and product types, from which we reveal an asymmetric generalization phenomenon: models trained on more liquid markets or products transfer well to less liquid ones, whereas the reverse transfer leads to substantial performance degradation.

q-fin.CP↗
arXiv2024

Singular Integrals associated with Reflection Groups on Euclidean Space

In the field of harmonic analysis, geometric considerations are frequently crucial. Specially, group actions such as translations, dilations and rotations on Euclidean space are instrumental. The objective of this paper is to extend the study of singular integrals to include the effects of group reflections on Euclidean space, and to establish the T1 theorem for these singular integrals.

math.CA↗
arXiv2024

Riesz transform and commutators in the Dunkl setting

In this paper we characterise the optimal pointwise size and regularity estimates for the Dunkl Riesz transform kernel involving both the Euclidean metric and the Dunkl metric, where these two metrics are not equivalent. We further establish a suitable version of the pointwise kernel lower bound of the Dunkl Riesz transform via the Euclidean metric only. Then we show that the lower bound of commutator of the Dunkl Riesz transform is with respect to the BMO space associated with the Euclidean metric, and that the upper bound is respect to the BMO space associated with the Dunkl metric. Moreover, the compactness and the two types of VMO are also addressed.

math.CA↗
arXiv2023

Lipschitz and Triebel--Lizorkin spaces, commutators in Dunkl setting

We first study the Lipschitz spaces $Λ_{d}^β$ associated with the Dunkl metric, $β\in(0,1)$, and prove that it is a proper subspace of the classical Lipschitz spaces $Λ^β$ on $\mathbb R^N$, as the Dunkl metric and the Euclidean metric are non-equivalent. Next, we further show that the Lipschitz spaces $Λ^β$ connects to the Triebel--Lizorkin spaces $\dot{ F}^{α,q}_{p,{\rm D}}$ associated with the Dunkl Laplacian $\triangle_{\rm D}$ in $\mathbb R^ N $ and to the commutators of the Dunkl Riesz transform and the fractional Dunkl Laplacian $\triangle_{\rm D}^{-α/2}$, $0<α<\textbf{N}$ (the homogeneous dimension for Dunkl measure), which is represented via the functional calculus of the Dunkl heat semigroup $e^{-t\triangle_{\rm D}}$. The key steps in this paper are a finer decomposition of the underlying space via Dunkl metric and Euclidean metric to bypass the use of Fourier analysis, and a discrete weak-type Calderón reproducing formula in these new Triebel--Lizorkin spaces $\dot{ F}^{α,q}_{p,{\rm D}}$.

math.FA↗
arXiv2022

Singular integral operators, $T1$ theorem, Littlewood-Paley theory and Hardy spaces in Dunkl Setting

The purpose of this paper is to introduce a new class of singular integral operators in the Dunkl setting involving both the Euclidean metric and the Dunkl metric. Then we provide the $T1$ theorem, the criterion for the boundedness on $L^2$ for these operators. Applying this singular integral operator theory, we establish the Littlewood-Paley theory and the Dunkl-Hardy spaces. As applications, the boundedness of singular integral operators, particularly, the Dunkl-Rieze transforms, on the Dunkl-Hardy spaces is given. The $L^2$ theory and the singular integral operator theory play crucial roles. New tools developed in this paper include the weak-type discrete Calderón reproducing formulae, new test functions, and distributions, the Littlewood-Paley, the wavelet-type decomposition, and molecule characterizations of the Dunkl-Hardy space, Coifman's approximation to the identity and the decomposition of the identity operator on $L^2$, Meyer's commutation Lemma, and new almost orthogonal estimates in the Dunkl setting.

math.CA↗
arXiv2020

Besov and Triebel-Lizorkin Spaces on Spaces of Homogeneous Type with Applications to Boundedness of Calderón-Zygmund Operators

In this article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (in)homogeneous Besov and Triebel-Lizorkin spaces are independent of the choices of both exp-ATIs (or exp-IATIs) and underlying spaces of distributions, and give some basic properties of these spaces. As applications, the authors show that some known function spaces coincide with certain special cases of Besov and Triebel-Lizorkin spaces and, moreover, obtain the boundedness of Calderón-Zygmund operators on these Besov and Triebel-Lizorkin spaces. All these results strongly depend on the geometrical properties, reflected via its dyadic cubes, of the considered space of homogeneous type. Comparing with the known theory of these spaces on metric measure spaces, a major novelty of this article is that all results presented in this article get rid of the dependence on the reverse doubling assumption of the considered measure of the underlying space and hence give a final real-variable theory of these function spaces on spaces of homogeneous type.

math.FA↗
arXiv2020

Maximal function, Littlewood--Paley theory, Riesz transform and atomic decomposition in the multi-parameter flag setting

In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood--Paley square function and area integral, Riesz transforms and the atomic decomposition in the multi-parameter flag setting. The novel ingredients in this paper include (1) establishing appropriate discrete Calderón reproducing formulae in the flag setting and a version of the Plancherel--Pólya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels and flag version of harmonic functions; (3) developing an atomic decomposition via the finite speed propagation and area function in terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the multi-parameter Hardy space with the flag structure.

math.CA↗
arXiv2019

A note on weak factorization of Meyer-type Hardy space via Cauchy integral operator

This paper provides a weak factorization for the Meyer-type Hardy space $H^1_b(\mathbb{R})$, and characterizations of its dual ${\rm BMO}_b(\mathbb{R})$ and its predual ${\rm VMO}_b(\mathbb{R})$ via boundedness and compactness of a suitable commutator with the Cauchy integral $\mathscr{C}_{\Gamma}$, respectively. Here $b(x)=1+iA'(x)$ where $A'\in L^{\infty}(\mathbb{R})$, and the Cauchy integral $\mathscr{C}_{\Gamma}$ is associated to the Lipschitz curve $\Gamma=\{x+iA(x)\, : \, x\in \mathbb{R}\}$.

math.CA↗
arXiv2018

Atomic decomposition of product Hardy spaces via wavelet bases on spaces of homogeneous type

We provide an atomic decomposition of the product Hardy spaces $H^p(\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\widetilde{X} = X_1 \times X_2$. Here each factor $(X_i,d_i,\mu_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss. These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt\"onen and their underlying reference dyadic grids. However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry out this program, we introduce product $(p,q)$-atoms on $\widetilde{X}$ and product atomic Hardy spaces $H^{p,q}_{{\rm at}}(\widetilde{X})$. As consequences of the atomic decomposition of $H^p(\widetilde{X})$, we show that for all $q > 1$ the product atomic Hardy spaces coincide with the product Hardy spaces, and we show that the product Hardy spaces are independent of the particular choices of both the wavelet bases and the reference dyadic grids. Likewise, the product Carleson measure spaces ${\rm CMO}^p(\widetilde{X})$, the bounded mean oscillation space ${\rm BMO}(\widetilde{X})$, and the vanishing mean oscillation space ${\rm VMO}(\widetilde{X})$, as defined by Han, Li, and Ward, are also independent of the particular choices of both wavelets and reference dyadic grids.

math.CA↗
arXiv2018

A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type

Let $(X,d,μ)$ be a space of homogeneous type, with the upper dimension $ω$, in the sense of R. R. Coifman and G. Weiss. Assume that $η$ is the smoothness index of the wavelets on $X$ constructed by P. Auscher and T. Hytönen. In this article, when $p\in(ω/(ω+η),1]$, for the atomic Hardy spaces $H_{\mathrm{cw}}^p(X)$ introduced by Coifman and Weiss, the authors establish their various real-variable characterizations, respectively, in terms of the grand maximal function, the radial maximal function, the non-tangential maximal functions, the various Littlewood-Paley functions and wavelet functions. This completely answers the question of R. R. Coifman and G. Weiss by showing that no any additional (geometrical) condition is necessary to guarantee the radial maximal function characterization of $H_{\mathrm{cw}}^1(X)$ and even of $H_{\mathrm{cw}}^p(X)$ with $p$ as above. As applications, the authors obtain the finite atomic characterizations of $H^p_{\mathrm{cw}}(X)$, which further induce some criteria for the boundedness of sublinear operators on $H^p_{\mathrm{cw}}(X)$. Compared with the known results, the novelty of this article is that $μ$ is not assumed to satisfy the reverse doubling condition and $d$ is only a quasi-metric, moreover, the range $p\in(ω/(ω+η),1]$ is natural and optimal.

math.CA↗
arXiv2017

A class of singular integrals associated with Zygmund dilations

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for these operators on $L^p, 1<p<\infty$, which covers those studied by Ricci--Stein \cite{RS} and Nagel--Wainger \cite{NW}

math.CA↗
arXiv2016

Marcinkiewicz multipliers and Lipschitz spaces on Heisenberg groups

The Marcinkiewicz multipliers are $L^{p}$ bounded for $1<p<\infty $ on the Heisenberg group $\mathbb{H}^{n}\simeq \mathbb{C}^{n}\times \mathbb{R}$ (Müller, Ricci and Stein \cite{MRS}). This is surprising in the sense that these multipliers are invariant under a two parameter group of dilations on $\mathbb{C}^{n}\times \mathbb{R}$, while there is \emph{no} two parameter group of \emph{automorphic} dilations on $\mathbb{H} ^{n}$. The purpose of this paper is to establish a theory of the flag Lipschitz space on the Heisenberg group $\mathbb{H}^{n}\simeq \mathbb{C}^{n}\times \mathbb{R}$ in the sense `intermediate' between the classical Lipschitz space on the Heisenberg group $\mathbb{H}^{n}$ and the product Lipschitz space on $\mathbb{C}^{n}\times \mathbb{R}$. We characterize this flag Lipschitz space via the Littelewood-Paley theory and prove that flag singular integral operators, which include the Marcinkiewicz multipliers, are bounded on these flag Lipschitz spaces.

math.FA↗