Jingwei Guo

activity

20102026

most citedThe Weyl formula for planar annuli

3 citations · 12 across the 17 of their papers we have counts for

collaborators

17 papers

math.CA2026

Boundedness of Multilinear Hilbert Transforms Along Moment Curves

Jingwei Guo, Xiaochun Li, Guoqing Zhan

We prove the boundedness of multilinear Hilbert transforms along moment curves by establishing uniform estimates for both translated and untranslated multilinear paraproducts and b…

math.NT2026

A multidimensional Szemerédi theorem in integers

Jingwei Guo, Changxing Miao, Guoqing Zhan

For any integer $n \geq 2$ , let $(m_{1}, \dots, m_{n})$ be a strictly increasing $n$ -tuple of positive integers. We show that any subset $A \subset [N]^{n}$ of density at least $(\log…

math.CA2025

Improvement of Pólya's conjecture for balls and cylinders

Jingwei Guo, Changxing Miao, Weiwei Wang +1

Pólya's conjecture on the eigenvalues of the Laplacian has been one of the core problems in spectral geometry. Building upon the recent breakthrough works on Pólya's conjecture for…

math.CA2023

A polynomial Roth theorem for corners in $R^{2}$ and a related bilinear singular integral operator

Xuezhi Chen, Jingwei Guo

We prove a quantitative Roth-type theorem for polynomial corners in $R^{2}$ . Let $P_{1}$ and $P_{2}$ be two linearly independent polynomials with zero constant term. We show tha…

math.CA2022

Some notes on endpoint estimates for pseudo-differential operators

Jingwei Guo, Xiangrong Zhu

We study the pseudo-differential operator \begin{equation*} T_a f\left(x\right)=\int_{\mathbb{R}^n}e^{ix\cdotξ}a\left(x,ξ\right)\widehat{f}\left(ξ\right)\,\textrm{d}ξ, \end{equatio…

math.NT2021

Lattice points in stretched finite type domains

J. Guo, T. Jiang

We study an optimal stretching problem, which is a variant lattice point problem, for convex domains in $R^{d}$ ( $d \geq 2$ ) with smooth boundary of finite type that are symm…

math.CA2020

Two bipolynomial Roth theorems in $R$

Xuezhi Chen, Jingwei Guo, Xiaochun Li

We give two Roth theorems, related to the nonlinear configuration $x$ , $x + P_{1} (t)$ , $x + P_{2} (t)$ involving two polynomials, for sets in $R$ of positive density and of fractio…

math.SP2019

A note on the Weyl formula for balls in $R^{d}$

Jingwei Guo

Let $B = {x \in R^{d} : ∣ x ∣ < R}$ ( $d \geq 3$ ) be a ball. We consider the Dirichlet Laplacian associated with $B$ and prove that its eigenvalue counting func…

math.SP2019★ 3 cited

The Weyl formula for planar annuli

Jingwei Guo, Wolfgang Müller, Weiwei Wang +1

We study the zeros of cross-product of Bessel functions and obtain their approximations, based on which we reduce the eigenvalue counting problem for the Dirichlet Laplacian associ…

math.NT2017★ 3 cited

Lattice points in stretched model domains of finite type in $R^{d}$

Jingwei Guo, Weiwei Wang

We study an optimal stretching problem for certain convex domain in $R^{d}$ ( $d \geq 3$ ) whose boundary has points of vanishing Gaussian curvature. We prove that the optimal…

math.NT2017

Lattice points in model domains of finite type in $R^{d}$ , II

Jingwei Guo, Tao Jiang

We study the lattice point problem associated with a special class of high-dimensional finite type domains via estimating the Fourier transforms of corresponding indicator function…

math.SP2017★ 1 cited

An improved remainder estimate in the Weyl formula for the planar disk

Jingwei Guo, Weiwei Wang, Zuoqin Wang

In \cite{colin}, Y. Colin de Verdière proved that the remainder term in the two-term Weyl formula for the eigenvalue counting function for the Dirichlet Laplacian associated with t…

math.NT2015

A note on lattice points in certain finite type domains in $R^{d}$

Jingwei Guo

We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.

math.CA2014★ 1 cited

Bilinear Hilbert transforms associated to plane curves

Jingwei Guo, Lechao Xiao

We prove that the bilinear Hilbert transforms and maximal functions along certain general plane curves are bounded from $L^{2} (R) \times L^{2} (R)$ to $L^{1} (R)$ …

math.NT2013★ 1 cited

Lattice points in rotated convex domains

Jingwei Guo

If $B \subset R^{d}$ ( $d ⩾ 2$ ) is a compact convex domain with a smooth boundary of finite type, we prove that for almost every rotation $θ \in S O (d)$ the rem…

math.NT2010★ 1 cited

Lattice points in large convex planar domains of finite type

Jingwei Guo

Let $B$ be a compact convex planar domain with smooth boundary of finite type and $B_{θ}$ its rotation by an angle $θ$ . We prove that for almost every $θ\in[0, 2π…

math.NT2010★ 2 cited

On lattice points in large convex bodies

Jingwei Guo

We consider a compact convex body $B$ in $R^{d}$ $(d ⩾ 3)$ with smooth boundary and nonzero Gaussian curvature and prove a new estimate of $P_{\mathcal{B}}(…

Boundedness of Multilinear Hilbert Transforms Along Moment Curves

A multidimensional Szemerédi theorem in integers

Improvement of Pólya's conjecture for balls and cylinders

A polynomial Roth theorem for corners in R2 and a related bilinear singular integral operator

Some notes on endpoint estimates for pseudo-differential operators

Lattice points in stretched finite type domains

Two bipolynomial Roth theorems in R

A note on the Weyl formula for balls in Rd

The Weyl formula for planar annuli

Lattice points in stretched model domains of finite type in Rd

Lattice points in model domains of finite type in Rd, II

An improved remainder estimate in the Weyl formula for the planar disk

A note on lattice points in certain finite type domains in Rd

Bilinear Hilbert transforms associated to plane curves

Lattice points in rotated convex domains

Lattice points in large convex planar domains of finite type

On lattice points in large convex bodies

A polynomial Roth theorem for corners in $R^{2}$ and a related bilinear singular integral operator

Two bipolynomial Roth theorems in $R$

A note on the Weyl formula for balls in $R^{d}$

Lattice points in stretched model domains of finite type in $R^{d}$

Lattice points in model domains of finite type in $R^{d}$ , II

A note on lattice points in certain finite type domains in $R^{d}$