8 citations · 47 across the 26 of their papers we have counts for
27 papers
Asymptotic Formulas for Negative Sobolev Norms and Applications
Huaiqian Li
This paper establishes an asymptotic formula for negative Sobolev norms as the fractional order tends to zero. In the Euclidean setting, under a mild boundedness condition, the pro…
On Limit Formulas for Besov Seminorms and Nonlocal Perimeters in the Dunkl Setting
Huaiqian Li, Bingyao Wu
We investigate the limiting behavior of Besov seminorms and nonlocal perimeters in Dunkl theory. The present work generalizes two fundamental results: the Maz'ya--Shaposhnikova for…
A Comprehensive End-to-End Computer Vision Framework for Restoration and Recognition of Low-Quality Engineering Drawings
Lvyang Yang, Jiankang Zhang, Huaiqiang Li +4
The digitization of engineering drawings is crucial for efficient reuse, distribution, and archiving. Existing computer vision approaches for digitizing engineering drawings typica…
Asymptotics of Kantorovich Distance for Empirical Measures of the Laguerre Model
Huaiqian Li, Bingyao Wu
We estimate the rate of convergence for the Kantorovich (or Wasserstein) distance between empirical measures of i.i.d. random variables associated with the Laguerre model of order…
Wasserstein Convergence for Empirical Measures of Subordinated Fractional Brownian Motions on the Flat Torus
Huaiqian Li, Bingyao Wu
We estimate rates of convergence for empirical measures associated with the subordinated fractional Brownian motion to the uniform distribution on the flat torus under the Wasserst…
Sharp Li--Yau Inequalities for Dunkl Harmonic Oscillators
Huaiqian Li, Bin Qian
We study the Li--Yau inequality for the heat equation corresponding to the Dunkl harmonic oscillator, which is a non-local Schrödinger operator parameterized by reflections and mul…
Wasserstein Convergence for Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds
Huaiqian Li, Bingyao Wu
We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold with boundary …
Wasserstein Convergence for Conditional Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds
Huaiqian Li, Bingyao Wu
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1},…
Wasserstein Convergence Rates for Empirical Measures of Subordinated Processes on Noncompact Manifolds
Huaiqian Li, Bingyao Wu
The asymptotic behaviour of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessar…
Li--Yau Inequalities for Dunkl Heat Equations
Huaiqian Li, Bin Qian
Motivated by recent works due to Yu--Zhao [J. Geom. Anal. 2020] and Weber--Zacher [arXiv:2012.12974], we study Li--Yau inequalities for the heat equation corresponding to the Dunkl…
Weak Type Estimates for Square Functions of Dunkl Heat Flows
Huaiqian Li
The weak boundedness of the Littlewood--Paley--Stein square function for the Dunkl heat flow is proved via estimates on the Dunkl heat kernel of integral type and the Caldr…
Dimension-Free Square Function Estimates for Dunkl Operators
Huaiqian Li, Mingfeng Zhao
Dunkl operators may be regarded as differential-difference operators parameterized by finite reflection groups and multiplicity functions. In this paper, the Littlewood--Paley squa…
Littlewood--Paley--Stein inequalities on spaces
Huaiqian Li
The boundedness on vertical Littlewood--Paley square functions for heat flows on spaces with is proved. With regards to the proof, f…
Weak Boundedness of Riesz Transforms on Vector Bundles
Huaiqian Li
The weak boundedness of (local) Riesz transforms corresponding to a large class of Schrödinger operators on vector bundles is proved, mainly assuming the generalized volume…
Weighted Littlewood--Paley inequalities for heat flows in $\RCD$ spaces
Huaiqian Li
We establish inequalities on vertical Littlewood--Paley square functions for heat flows in the weighted space over metric measure spaces satisfying the $\RCD^\ast(0,N)$ condi…
Littlewood--Paley--Stein Estimates for Non-local Dirichlet Forms
Huaiqian Li, Jian Wang
We obtain the boundedness in spaces for all of the so-called vertical Littlewood--Paley functions for non-local Dirichlet forms in the metric measure space under…
Quantitative stability estimates for Fokker-Planck equations
Huaiqian Li, Dejun Luo
We consider the Fokker--Planck equations with irregular coefficients. Two different cases are treated: in the degenerate case, the coefficients are assumed to be weakly differentia…
Sharp Heat Kernel Bounds and Entropy in Metric Measure Spaces
Huaiqian Li
We establish sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying $\RCD(0,N)$ ( equivalently, $\RCD^\ast(0,N)$) condition with $…
Lower Bound Estimates for The First Eigenvalue of The Weighted -Laplacian on Smooth Metric Measure Spaces
Yuzhao Wang, Huaiqian Li
New lower bounds of the first nonzero eigenvalue of the weighted -Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumpt…
Heat Kernel Bounds on Metric Measure Spaces and Some Applications
Renjin Jiang, Huaiqian Li, Huichun Zhang
Let be a space with and . For , we derive the upper and lower bounds of the heat kernel on …
Harnack Inequalities for SDEs with Multiplicative Noise and Non-regular Drift
Huaiqian Li, Dejun Luo, Jian Wang
The log-Harnack inequality and Harnack inequality with powers for semigroups associated to SDEs with non-degenerate diffusion coefficient and non-regular time-dependent drift coeff…
Heat kernel upper bounds under the generalized curvature(-dimension) inequality
Huai Qian LI
In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic o…
Dimension free Harnack inequalities on $\RCD(K, \infty)$ spaces
Huaiqian Li
The dimension free Harnack inequality for the heat semigroup is established on the $\RCD(K,\infty)$ space, which is a non-smooth metric measure space having the Ricci curvature bou…
A probabilistic proof of the fundamental gap conjecture via the coupling by reflection
Fuzhou Gong, Huaiqian Li, Dejun Luo
Let be a strictly convex domain with smooth boundary and diameter . The fundamental gap conjecture claims that if is convex, then t…