Sung-Yi Liao

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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…

Sharp derivative inequalities for maximal functions

Sharp higher order regularity of discrete maximal functions

On L2 estimates for quadratic images of product Frostman measures

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