8 papers
On the endpoint estimate for discrete spherical average over sparse sequences
Sanghyuk Lee, Ji Li, Chong-wei Liang +1
Let . For a lacunary sequence of radii in the \emph{highly composite} regime, that is with as ,…
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 JanÄar, for , and establish the boundedness on f…