Shaoming Guo

activity

20142026

most citedMaximal operators and Hilbert transforms along variable non-flat homogeneous curves

35 citations · 210 across the 41 of their papers we have counts for

collaborators

44 papers

math.CA2026

On planar Nikodym-type sets

Alan Chang, Mingfeng Chen, Shaoming Guo +3

Nikodym constructed a measure-zero Borel set in the plane that contains a punctured line segment passing through each point in the unit square. Fenton and Falconer asked whether a…

math.CA2023

A multi-parameter cinematic curvature

Mingfeng Chen, Shaoming Guo, Tongou Yang

We state a multi-parameter cinematic curvature condition, and prove $L^{p}$ bounds for related maximal operators. In particular, we verify a local smoothing conjecture of Zahl.

math.CA2022

A restricted projection problem for fractal sets in $R^{n}$

Shengwen Gan, Shaoming Guo, Hong Wang

Let $γ : [- 1, 1] \to R^{n}$ be a smooth curve that is non-degenerate. Take $m \leq n$ and a Borel set $E \subset [0, 1]^{n}$ . We prove that the orthogonal projection of $E$ to the…

math.CA2022

A dichotomy for Hörmander-type oscillatory integral operators

Shaoming Guo, Hong Wang, Ruixiang Zhang

In this paper, we first generalize the work of Bourgain and state a curvature condition for Hörmander-type oscillatory integral operators, which we call Bourgain's condition. This…

math.CA2022★ 3 cited

On restricted projections to planes in $R^{3}$

Shengwen Gan, Shaoming Guo, Larry Guth +3

Let $γ : [0, 1] \to S^{2}$ be a non-degenerate curve in $R^{3}$ , that is to say, $det (γ (θ), γ^{'} (θ), γ " (θ)) \neq = 0$ . For each $θ \in [0, 1]$ , let $V_θ=γ(θ)^\pe…

math.CA2021★ 1 cited

On the strict majorant property in arbitrary dimensions

Philip T. Gressman, Shaoming Guo, Lillian B. Pierce +2

In this work we study $d$ -dimensional majorant properties. We prove that a set of frequencies in $Z^{d}$ satisfies the strict majorant property on $L^{p} ([0, 1]^{d})$ for all $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.NT2021★ 1 cited

Improved discrete restriction for the parabola

Shaoming Guo, Zane Kun Li, Po-Lam Yung

Using ideas from Guth-Maldague-Wang and working over $Q_{p}$ , we show that the discrete restriction constant for the parabola is $O_{\varepsilon}((\log M)^{2 + \varepsilon})…

math.CA2021★ 1 cited

A stationary set method for estimating oscillatory integrals

Saugata Basu, Shaoming Guo, Ruixiang Zhang +1

We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarry's problems in dimen…

math.CA2021★ 9 cited

Sharp $L^{p}$ bounds for the helical maximal function

David Beltran, Shaoming Guo, Jonathan Hickman +1

We establish the $L^{p} (R^{3})$ boundedness of the helical maximal function for the sharp range $p > 3$ . Our results improve the previous known bounds for $p > 4$ . The key ingredi…

math.CA2021

Sobolev improving for averages over curves in $R^{4}$

David Beltran, Shaoming Guo, Jonathan Hickman +1

We study $L^{p}$ -Sobolev improving for averaging operators $A_{γ}$ given by convolution with a compactly supported smooth density $μ_{γ}$ on a non-degenerate curve. In particular, in 4 d…

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

A variable coefficient multi-frequency lemma

Shaoming Guo, Pavel Zorin-Kranich

We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by K…

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

The circular maximal operator on Heisenberg radial functions

David Beltran, Shaoming Guo, Jonathan Hickman +1

Lebesgue space estimates are obtained for the circular maximal function on the Heisenberg group $H^{1}$ restricted to a class of Heisenberg radial functions. Under this assu…

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

On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets

Shaoming Guo, Tian Lan, Yakun Xi

We give a complete characterization of the size of Borel sets that are mid-point convex but not (essentially) convex, in terms of their Hausdorff dimensions and Hausdorff measures.

math.CA2019★ 15 cited

Reversing a philosophy: from counting to square functions and decoupling

Philip T. Gressman, Shaoming Guo, Lillian B. Pierce +2

Breakthrough work of Bourgain, Demeter, and Guth recently established that decoupling inequalities can prove powerful results on counting integral solutions to systems of Diophanti…

math.CA2019★ 5 cited

A bilinear proof of decoupling for the cubic moment curve

Shaoming Guo, Zane Kun Li, Po-Lam Yung

Using a bilinear method that is inspired by the method of efficient congruencing of Wooley [Woo16], we prove a sharp decoupling inequality for the moment curve in $R^{3}$ .

math.CA2019★ 6 cited

Maximal functions associated with families of homogeneous curves: $L^{p}$ bounds for $p \leq 2$

Shaoming Guo, Joris Roos, Andreas Seeger +1

Let $M^{(u)}$ , $H^{(u)}$ be the maximal operator and Hilbert transform along the parabola $(t, u t^{2})$ . For $U \subset (0, \infty)$ we consider $L^{p}$ estimates for the maximal functio…

math.CA2019

Polynomial Roth theorems on sets of fractional dimensions

Robert Fraser, Shaoming Guo, Malabika Pramanik

Let $E \subset R$ be a closed set of Hausdorff dimension $α \in (0, 1)$ . Let $P : R \to R$ be a polynomial without a constant term whose degree is bigger tha…

math.CA2019★ 7 cited

Decoupling for certain quadratic surfaces of low co-dimensions

Shaoming Guo, Pavel Zorin-Kranich

We prove sharp $ℓ^{p} L^{p}$ decoupling inequalities for $2$ quadratic forms in $4$ variables. We also recover several previous results (arXiv:1409.1634, arXiv:1501.07224, arXiv:…

math.CA2019★ 8 cited

A maximal function for families of Hilbert transforms along homogeneous curves

Shaoming Guo, Joris Roos, Andreas Seeger +1

Let $H^{(u)}$ be the Hilbert transform along the parabola $(t, u t^{2})$ where $u \in R$ . For a set $U$ of positive numbers consider the maximal function $\mathcal{H}^U \!f= \s…

On planar Nikodym-type sets

A multi-parameter cinematic curvature

A restricted projection problem for fractal sets in Rn

A dichotomy for Hörmander-type oscillatory integral operators

On restricted projections to planes in R3

On the strict majorant property in arbitrary dimensions

The Bochner-Riesz problem: an old approach revisited

Improved discrete restriction for the parabola

A stationary set method for estimating oscillatory integrals

Sharp Lp bounds for the helical maximal function

Sobolev improving for averages over curves in R4

Decoupling inequalities for quadratic forms

A variable coefficient multi-frequency lemma

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

A restriction estimate for surfaces with negative Gaussian curvatures

The circular maximal operator on Heisenberg radial functions

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

On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets

Reversing a philosophy: from counting to square functions and decoupling

A bilinear proof of decoupling for the cubic moment curve

Maximal functions associated with families of homogeneous curves: Lp bounds for p≤2

Polynomial Roth theorems on sets of fractional dimensions

Decoupling for certain quadratic surfaces of low co-dimensions

A maximal function for families of Hilbert transforms along homogeneous curves

A restricted projection problem for fractal sets in $R^{n}$

On restricted projections to planes in $R^{3}$

Sharp $L^{p}$ bounds for the helical maximal function

Sobolev improving for averages over curves in $R^{4}$

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

Maximal functions associated with families of homogeneous curves: $L^{p}$ bounds for $p \leq 2$