Shengwen Gan

collaborators

4 papers

math.CA2024

Kakeya problem and projection problem for $k$ -geodesics in Grassmannians

Shengwen Gan

The Kakeya problem in $R^{n}$ is about estimating the size of union of $k$ -planes; the projection problem in $R^{n}$ is about estimating the size of projection of a s…

math.CA2024

A weighted decoupling inequality and its application to the maximal Bochner-Riesz problem

Shengwen Gan, Shukun Wu

We prove some weighted $L^{p} ℓ^{p}$ -decoupling estimates when $p = 2 n / (n - 1)$ . As an application, we give a result beyond the real interpolation exponents for the maximal Bochner-Riesz…

math.CA2023

A Marstrand projection theorem for lines

Shengwen Gan

Fix integers $1 < k < n$ . For $V \in G (k, n)$ , let $P_{V} : R^{n} \to V$ be the orthogonal projection. For $V \in G (k, n)$ , define the map \[ π_V: A(1,n)\rightarrow A(1,V)\bigsq…

math.CA2023

Restriction estimates for quadratic manifolds of arbitrary codimensions

Shengwen Gan, Larry Guth, Changkeun Oh

The restriction conjecture is one of the famous problems in harmonic analysis. There have been many methods developed in the study of the conjecture for the paraboloid. In this pap…

Kakeya problem and projection problem for k-geodesics in Grassmannians

A weighted decoupling inequality and its application to the maximal Bochner-Riesz problem

A Marstrand projection theorem for lines

Restriction estimates for quadratic manifolds of arbitrary codimensions

Kakeya problem and projection problem for $k$ -geodesics in Grassmannians