Changkeun Oh

activity

20162026

most citedDecouplings for three-dimensional surfaces in

R^{6}

6 citations · 22 across the 13 of their papers we have counts for

collaborators

15 papers

math.CA2026

Sharp rational points counting near nondegenerate curves in $R^{n}$

Shengwen Gan, Shaoming Guo, Changkeun Oh

We establish sharp bounds for rational points near compact smooth nondegenerate curves in $R^{n}$ , for every $n \geq 4$ . For a nondegenerate curve $C$ in $R^{n}$ …

math.CA2026

Positive measure for restricted projections along smooth non-degenerate curves

Seonghun Jeon, Changkeun Oh

Let $1 \leq m < n$ , and let $γ : [0, 1] \to R^{n}$ be a smooth non-degenerate curve. For $θ \in [0, 1]$ , set \[ V_θ := \operatorname{span} \{γ'(θ),\ldots,γ^{(m)}(θ)\}, \] and let $π_{θ}$ …

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…

math.CA2023★ 1 cited

Small cap decoupling for the paraboloid in $R^{n}$

Larry Guth, Dominique Maldague, Changkeun Oh

We extend the small cap decoupling program established by Demeter, Guth, and Want to paraboloids in $R^{n}$ for some range of $p$ .

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

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.CA2021

An improved bilinear restriction estimate for the paraboloid in $R^{3}$

Changkeun Oh

We obtain a sharp bilinear restriction estimate for the paraboloid in $R^{3}$ for $q > 3.25$ .

math.CA2020★ 5 cited

Decoupling inequalities for quadratic forms

Shaoming Guo, Changkeun Oh, Ruixiang Zhang +1

We prove sharp $ℓ^{q} L^{p}$ decoupling inequalities for $p, q \in [2, \infty)$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for qu…

math.CA2020

Fourier restriction estimates for surfaces of co-dimension two in $R^{5}$

Shaoming Guo, Changkeun Oh

We prove $L^{p} \to L^{q}$ Fourier restriction estimates for 3-dimensional quadratic surfaces in $R^{5}$ . Our results are sharp, up to endpoints, for a few classes of su…

math.CA2020

A restriction estimate for surfaces with negative Gaussian curvatures

Shaoming Guo, Changkeun Oh

We prove $L^{p}$ bounds for the Fourier extension operators associated to surfaces in $R^{3}$ with negative Gaussian curvatures for every $p > 3.25$ .

math.CA2019★ 6 cited

Decoupling for two quadratic forms in three variables: a complete characterization

Shaoming Guo, Changkeun Oh, Joris Roos +2

We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in $R^{5}$ given by two quadratic forms in three variables. Together with previous work…

math.CA2019

Small cap decoupling inequalities: Bilinear methods

Changkeun Oh

We obtain sharp small cap decoupling inequalities associated to the moment curve for certain range of exponents $p$ . Our method is based on the bilinearization argument due to Bour…

math.CA2016★ 6 cited

Decouplings for three-dimensional surfaces in $R^{6}$

Changkeun Oh

We obtain the sharp $l^{p}$ decoupling for three-dimensional nondegenerate surfaces in $R^{6}$ . This can be thought of as a generalization of Bourgain and Demeter's result, wh…

math.CA2016★ 3 cited

Remarks on Wolff's inequality for hypersurfaces

Shaoming Guo, Changkeun Oh

We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for $k$ -cones. These are extensions of results…

Sharp rational points counting near nondegenerate curves in Rn

Positive measure for restricted projections along smooth non-degenerate curves

Restriction estimates for quadratic manifolds of arbitrary codimensions

Small cap decoupling for the paraboloid in Rn

New bounds for Stein's square functions in higher dimensions

A note on local smoothing estimates for fractional Schrödinger equations

The Bochner-Riesz problem: an old approach revisited

An improved bilinear restriction estimate for the paraboloid in R3

Decoupling inequalities for quadratic forms

Fourier restriction estimates for surfaces of co-dimension two in R5

A restriction estimate for surfaces with negative Gaussian curvatures

Decoupling for two quadratic forms in three variables: a complete characterization

Small cap decoupling inequalities: Bilinear methods

Decouplings for three-dimensional surfaces in R6

Remarks on Wolff's inequality for hypersurfaces

Sharp rational points counting near nondegenerate curves in $R^{n}$

Small cap decoupling for the paraboloid in $R^{n}$

An improved bilinear restriction estimate for the paraboloid in $R^{3}$

Fourier restriction estimates for surfaces of co-dimension two in $R^{5}$

Decouplings for three-dimensional surfaces in $R^{6}$