Liang-Chuan Wu

activity

20242026

collaborators

13 papers

stat.ME2026

An Algebraic Approach to Constrained K-means Clustering

Hiroki Oohori, Kentaro Fukushima, Michio Yamamoto

Clustering is typically performed using only object features, although additional information about relationships between objects may be available and can be incorporated through c…

math.CA2026

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

Yuying Chen, Yanchang Han, Yongsheng Han +2

We prove a Fefferman--Stein good- $λ$ inequality for the Dunkl Poisson semigroup associated with a finite reflection group and a non-negative multiplicity function. For arbitrary co…

math.CA2026

Two-weight commutators for the Bessel Riesz transform with Andersen--Kerman weights

Ji Li, Chong-Wei Liang, Chaojie Wen +1

Let $α > - 1/2$ , $α \neq = 0$ , and let $Δ_{α} = - \frac{d ^{2}}{d x ^{2}} - \frac{2 α}{x} \frac{d}{d x}$ be the Bessel operator on $R_{+} = (0, \infty)$ . We characterize boundedness and compactness…

math.CA2026

Chamber lifting and non-radial Dunkl multipliers

Der-Chen Chang, Ji Li, Chaojie Wen +1

We study non-radial Dunkl multipliers via chamber lifting. For an arbitrary finite reflection group $G$ , the chamber lifting records all reflected values of a function and conjugat…

math.CA2026

Two-weight inequalities for the Dunkl--Poisson integrals

Qingdong Guo, Ji Li, Brett D. Wick +1

We prove an $L^{2}$ two-weight testing theorem for the Dunkl--Poisson semigroup. The difficulty is geometric. The Dunkl orbit distance has several reflected diagonals, so a single or…

math.CA2026

Calderon-type commutators and chamber lifting in the Dunkl setting

Yongsheng Han, Ming-Yi Lee, Ji Li +2

Let $G$ be a finite reflection group, and let $T_{j}$ , $Δ_{κ}$ , and $d ω$ denote its Dunkl operators, Laplacian, and measure, respectively. Write $R_{j} = - T_{j} (- Δ_{κ})^{- 1/2}$ for th…

math.CA2026

Haar bases for multi-parameter twisted structures

Ji Li, Chong-Wei Liang, Brett D. Wick +2

Motivated by the Cauchy--Szegő projections on a broad class of Siegel domains and the geometric quotient structures of nilpotent Lie groups observed by Nagel, Ricci, and Stein, we…

math.CA2025

Endpoint boundedness of singular integrals: CMO space associated to Schrödinger operators

Xueting Han, Ji Li, Liangchuan Wu

Let $L = - Δ + V$ be a Schrödinger operator acting on $L^{2} (R^{n})$ , where the nonnegative potential $V$ belongs to the reverse Hölder class $R H_{q}$ for some $…

math.CA2025

The fractional Riesz transform and their commutator in Dunkl setting

Yanping Chen, Xueting Han, Liangchuan Wu

In this paper, we study the boundedness of the fractional Riesz transforms in the Dunkl setting. Moreover, we establish the necessary and sufficient conditions for the boundedness…

math.AP2024

Hölder regularity and Liouville Theorem for the Schrödinger equation with certain critical potentials, and applications to Dirichlet problems

Bo Li, Ji Li, Liangchuan Wu

Let $(X, d, μ)$ be a metric measure space satisfying a doubling property with the upper/lower dimension $Q \geq n > 1$ , and admitting an $L^{2}$ -Poincaré inequality. In this article, we es…

math.CA2024

On maximal functions generated by Hörmander-type spectral multipliers

Peng Chen, Xixi Lin, Liangchuan Wu +1

Let $(X, d, μ)$ be a metric space with doubling measure and $L$ be a nonnegative self-adjoint operator on $L^{2} (X)$ whose heat kernel satisfies the Gaussian upper bound. We assume tha…

math.AP2024

Global-in-time maximal regularity for the Cauchy problem of the heat equation in BMO and applications

Xuan Thinh Duong, Ji Li, Liangchuan Wu +1

In this article, we establish global-in-time maximal regularity for the Cauchy problem of the classical heat equation $\partial_{t} u (x, t) - Δ u (x, t) = f (x, t)$ with $u (x, 0) = 0$ in a certai…

math.CA2024

Schatten classes and commutators in the two weight setting, II. Riesz transforms

Michael Lacey, Ji Li, Brett D. Wick +1

We characterize the Schatten class $S^{p}$ of the commutator of Riesz transforms $[b, R_{j}]$ in $R^{n}$ ( $j = 1, \dots, n$ ) in the two weight setting for $n < p < \infty$ , by introduc…