6 papers · 1 filter
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…
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…
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…