Sung-Yi Liao

collaborators

4 papers

math.CA2026

Sharp derivative inequalities for maximal functions

Sung-Yi Liao, José Madrid, Eyvindur Ari Palsson

We determine the optimal constant in the $L^{p}$ -derivative inequality for the uncentered Hardy--Littlewood maximal operator on the real line for every $1 < p < \infty$ . It is the unique…

math.CA2026

Sharp higher order regularity of discrete maximal functions

Sung-Yi Liao, José Madrid, Eyvindur Palsson +1

We derive sharp $ℓ^{p} (Z)$ bounds for the $k$ th derivative of the discrete uncentered maximal operator applied to characteristic functions $f : Z \to {0, 1}$ in the…

math.CA2026

On $L^{2}$ estimates for quadratic images of product Frostman measures

Sung-Yi Liao, Thang Pham, Chun-Yen Shen

Let $f \in R [x, y, z]$ be a fixed non-degenerate quadratic polynomial. Given an $α$ -Frostman probability measure $μ$ supported on $[0, 1]$ with $α \in (0, 1)$ , consider the pushfor…

math.CO2023

Exploration on Incidence Geometry and Sum-Product Phenomena

Sung-Yi Liao

In additive combinatorics, Erdös-Szemerédi Conjecture is an important conjecture. It can be applied to many fields, such as number theory, harmonic analysis, incidence geometry, an…

Sharp derivative inequalities for maximal functions

Sharp higher order regularity of discrete maximal functions

On L2 estimates for quadratic images of product Frostman measures

Exploration on Incidence Geometry and Sum-Product Phenomena

On $L^{2}$ estimates for quadratic images of product Frostman measures