Guangzeng Yi

activity

20242026

collaborators

3 papers

math.CA2026

Two-ends Furstenberg inequality for transversal families and applications to Fourier decay

William O'Regan, Shukun Wu, Guangzeng Yi

We generalise the recent two-ends Furstenberg inequality due to Wang and the second author from lines to a family of transversal curves, and give a much simplified proof. As an app…

math.CA2025

Furstenberg set theorem for transversal families of functions

Tuomas Orponen, Aleksi PyÃ¶rÃ¤lÃ¤, Guangzeng Yi

We prove an extension of the Furstenberg set theorem to families of graphs satisfying a transversality condition. We apply the result to derive bounds on $L^{p}$ -norms of Fourier t…

math.CA2024

On bounded energy of convolution of fractal measures

Guangzeng Yi

For all $s \in [0, 1]$ and $t \in (0, s] \cup [2 - s, 2)$ , we find the supremum of numbers $I ¨ \in (0, 2)$ such that $I_{I ¨} (I^¼ * I ¨ ) ≲ 1$ , where $I^¼$ is any Borel measure on $B(1)…