Chong-Wei Liang

activity

20212026

collaborators

15 papers

math.CA2026

On the endpoint estimate for discrete spherical average over sparse sequences

Sanghyuk Lee, Ji Li, Chong-Wei Liang +2

Let $d \geq 5$ , and let $A_{λ}$ denote the normalized discrete spherical average on $Z^{d}$ with squared radius $λ$ . For a strictly increasing sequence $(μ_{k})$ of positive intege…

math.DS2026

On the Hausdorff measure of projections of self-similar sets

Chong-Wei Liang

For $0 < d \leq 1/4$ , let $C (d)$ be the four-corner Cantor set with Hausdorff dimension $s_{d} = lo g 4/ lo g (1/ d)$ . Peres, Simon, and Solomyak, as well as Mattila, asked for whic…

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.CO2026

Peres--Schlag's nonempty-interior problem and a shifted-product variant for product sets

Guo-Dong Hong, Chong-Wei Liang, Chun-Yen Shen

We study finite-field analogues of the Peres--Schlag nonempty-interior problem for product sets. Given $A\subseteq\mathbb F_p$, we ask when a suitable one-dimensional linear imag…

math.CA2026

On the Peres--Schlag orthogonal projection problem and Kakeya-type sets

Guo-Dong Hong, Chong-Wei Liang, Chun-Yen Shen

We investigate the Peres--Schlag nonempty interior problem for orthogonal projections in both the finite-field and Euclidean settings. Over finite fields $F_{q}^{n}$ , we employ…

math.CA2026

A curved three-point pattern problem for fractal sets on the real line

Surjeet Singh Choudhary, Chong-Wei Liang, Chun-Yen Shen

We study the occurrence of curved three-point configurations in fractal subsets of the real line. We prove that if $E \subset [0,1]$ is a compact set with sufficiently large Haus…

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.CA2026

Maximal functions with twisted structures, distribution inequality and applications

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

Motivated by the geometric reduction of Cauchy--Szegő projections on quadratic surfaces of higher codimension (Nagel--Ricci--Stein, 2001) and recent developments on the real-variab…

math.CA2026

Twisted Multiparameter singular integrals -- real variable methods and applications, I

Zunwei Fu, Ji Li, Chong-Wei Liang +2

In this paper, we introduce a class of twisted multiparameter singular integrals on $R^{2 m}$ , motivated by the Cauchy--Szegő projections and the solving operators for $\ba…

math.GR2026

The Brascamp--Lieb inequality on compact Lie groups and its extinction on homogeneous Lie groups

Michael G. Cowling, Ji Li, Chong-Wei Liang

We study the Brascamp--Lieb inequalities on locally compact nonabelian groups and the Brascamp--Lieb constants $BL (G, σ, p)$ associated to a Brasca…

math.CA2025

Lacunary $δ$ -Discretised Spherical Maximal Operators

Surjeet Singh Choudhary, Ji Li, Chong-Wei Liang +1

We study the lacunary analogue of the $δ$ -discretised spherical maximal operators introduced by Hickman and Jančar, for $δ \in (0, 1/2)$ , and establish the boundedness on $L^{p}$ for…

math.CO2025

On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method

Ji Li, Chong-Wei Liang, Chun-Yen Shen

The Falconer distance problem for Cartesian product sets was introduced and studied by Iosevich and Liu (\cite{MR3525385}). In this paper, by implementing a new observation on Cart…

math.CA2024

Muckenhoupt-Type Weights and Quantitative Weighted Estimate in the Bessel Setting

Ji Li, Chong-Wei Liang, Chun-Yen Shen +1

Part of the intrinsic structure of singular integrals in the Bessel setting is captured by Muckenhoupt-type weights. Anderson--Kerman showed that the Bessel Riesz transform is boun…

math.CA2023

Muckenhoupt-type weights and the intrinsic structure in Bessel Setting

Ji Li, Chong-Wei Liang, Fred Yu-Hsiang Lin +1

Fix $λ > - 1/2$ and $λ \neq = 0$ . Consider the Bessel operator (introduced by Muckenhoupt--Stein) $△_{λ} := - \frac{d ^{2}}{d x ^{2}} - \frac{2 λ}{x} \frac{d}{d x}$ on $R_{+} := (0, \infty)$ …

math.CA2021

A weak type estimate for regular fractional sparse operators

Ji Li, Chung-Wei Liang, Chun-Yen Shen

In this note the weak type estimates for fractional integrals are studied. More precisely, we adapt the arguments of Domingo-Salazar, Lacey, and Rey to obtain improvements for the…

On the endpoint estimate for discrete spherical average over sparse sequences

On the Hausdorff measure of projections of self-similar sets

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

Peres--Schlag's nonempty-interior problem and a shifted-product variant for product sets

On the Peres--Schlag orthogonal projection problem and Kakeya-type sets

A curved three-point pattern problem for fractal sets on the real line

Haar bases for multi-parameter twisted structures

Maximal functions with twisted structures, distribution inequality and applications

Twisted Multiparameter singular integrals -- real variable methods and applications, I

The Brascamp--Lieb inequality on compact Lie groups and its extinction on homogeneous Lie groups

Lacunary δ-Discretised Spherical Maximal Operators

On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method

Muckenhoupt-Type Weights and Quantitative Weighted Estimate in the Bessel Setting

Muckenhoupt-type weights and the intrinsic structure in Bessel Setting

A weak type estimate for regular fractional sparse operators

Lacunary $δ$ -Discretised Spherical Maximal Operators