Shukun Wu

activity

20192026

most citedOn the Bochner-Riesz operator in

R^{3}

5 citations · 14 across the 14 of their papers we have counts for

collaborators

14 papers

math.CA2026

Near diagonal additive energy bound for points on algebraic surfaces

Yifan Jing, Shukun Wu

Let $F : R^{3} \to R$ be a polynomial that is irreducible over $R$ with $deg F \geq 2$ . We prove that, for any finite $X \subset Z (F)$ that does not concen…

math.CA2026

Kakeya sets and dimension compression in compact Lie groups

Yifan Jing, Shukun Wu

We study two Kakeya set problems in compact semisimple Lie groups. In the first, motivated by the group structure, a Kakeya set is required to contain a left coset of every closed…

math.CA2022

Kakeya sets from lines in $S L_{2}$

Nets Hawk Katz, Shukun Wu, Joshua Zahl

We prove that every Kakeya set in $R^{3}$ formed from lines of the form $(a, b, 0) + span (c, d, 1)$ with $a d - b c = 1$ must have Hausdorff dimension $3$ ; Kakeya sets…

math.CA2022

An improved restriction estimate in $R^{3}$

Hong Wang, Shukun Wu

We improve the $L^{p} \to L^{p}$ restriction estimate in $R^{3}$ to the range $p > 3 + 3/14$ , based on some Kakeya type incidence estimates and the refined decoupling theor…

math.CA2022

Square function estimates for conical regions

Shengwen Gan, Shukun Wu

We prove square function estimates for certain conical regions. Specifically, let ${Δ_{j}}$ be regions of the unit sphere $S^{n - 1}$ and let $S_{j} f$ be the smooth Fourier r…

math.PR2022★ 2 cited

Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets

Renming Song, Peixue Wu, Shukun Wu

Let $D$ be an open set of $R^{d}$ , $α \in (0, 2)$ and let $L_{α}^{D}$ be the generator of the censored $α$ -stable process in $D$ . In this paper, we establish sharp two-…

math.CA2021★ 1 cited

New bounds for Stein's square functions in higher dimensions

Shengwen Gan, Changkeun Oh, Shukun Wu

We improve the $L^{p} (R^{n})$ bounds on Stein's square function to the best-known range of the Fourier restriction problem when $n \geq 4$ . Applications including certain local…

math.CA2021

A note on local smoothing estimates for fractional Schrödinger equations

Shengwen Gan, Changkeun Oh, Shukun Wu

We improve local smoothing estimates for fractional Schrödinger equations for $α \in (0, 1) \cup (1, \infty)$ .

math.CA2021★ 2 cited

New bounds for Stein's square function in $R^{3}$

Shengwen Gan, Yifan Jing, Shukun Wu

We prove new $L^{p} (R^{3})$ bounds on Stein's square function for $p \geq 3.25$ . As an application, it improves the maximal Bochner-Riesz conjecture to the same range of $p$ .

math.CA2021

The Bochner-Riesz problem: an old approach revisited

Shaoming Guo, Changkeun Oh, Hong Wang +2

We show that the recent techniques developed to study the Fourier restriction problem apply equally well to the Bochner-Riesz problem. This is achieved via applying a pseudo-confor…

math.CO2020

A note on the largest sum-free sets of integers

Yifan Jing, Shukun Wu

Given $A$ a set of $N$ positive integers, an old question in additive combinatorics asks that whether $A$ contains a sum-free subset of size at least $N /3 + ω (N)$ for some increasing…

math.CA2020★ 5 cited

On the Bochner-Riesz operator in $R^{3}$

Shukun Wu

We improve the Bochner-Riesz conjecture in $R^{3}$ to $max {p, p / (p - 1)} \geq 3.25$ .

math.CA2020★ 3 cited

A note on the refined Strichartz estimates and maximal extension operator

Shukun Wu

There are two parts for this paper. In the first part, we extend some results in a recent paper by Du, Guth, Li and Zhang to a more general class of phase functions. The main metho…

math.CA2019★ 1 cited

New estimates of maximal Bochner-Riesz operator in the plane

Xiaochun Li, Shukun Wu

We prove some new $L^{p}$ estimates for maximal Bochner-Riesz operator in the plane.

Near diagonal additive energy bound for points on algebraic surfaces

Kakeya sets and dimension compression in compact Lie groups

Kakeya sets from lines in SL2​

An improved restriction estimate in R3

Square function estimates for conical regions

Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in C1,β open sets

New bounds for Stein's square functions in higher dimensions

A note on local smoothing estimates for fractional Schrödinger equations

New bounds for Stein's square function in R3

The Bochner-Riesz problem: an old approach revisited

A note on the largest sum-free sets of integers

On the Bochner-Riesz operator in R3

A note on the refined Strichartz estimates and maximal extension operator

New estimates of maximal Bochner-Riesz operator in the plane

Kakeya sets from lines in $S L_{2}$

An improved restriction estimate in $R^{3}$

Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets

New bounds for Stein's square function in $R^{3}$

On the Bochner-Riesz operator in $R^{3}$