9 papers
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…
On the endpoint estimate for discrete spherical average over sparse sequences
Sanghyuk Lee, Ji Li, Chong-Wei Liang +2
Let , and let denote the normalized discrete spherical average on with squared radius . For a strictly increasing sequence of positive intege…
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…
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 , we employ…
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…
Maximal Averages on the Affine Group and applications
Ji Li, Chun-Yen Shen, Chaojie Wen
Let \(G_n=\mathbb R^n\rtimes\mathbb R_+\) be equipped with the left Haar measure \( dμ(x,y)=\frac{dx\,dy}{y^{n+1}}. \) We study maximal averages associated with three basic motions…
Lacunary -Discretised Spherical Maximal Operators
Surjeet Singh Choudhary, Ji Li, Chong-Wei Liang +1
We study the lacunary analogue of the -discretised spherical maximal operators introduced by Hickman and Jančar, for , and establish the boundedness on for…
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…
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…