Xiaochun Li

activity

20032020

most citedOn a Conjecture of EM Stein on the Hilbert Transform on Vector Fields

35 citations · 82 across the 13 of their papers we have counts for

collaborators

13 papers

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.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.

math.CA2018★ 5 cited

Pointwise convergence of Schrödinger solutions and multilinear refined Strichartz estimates

Xiumin Du, Larry Guth, Xiaochun Li +1

We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geq…

math.NT2017★ 4 cited

Improved estimates for polynomial Roth type theorems in finite fields

Dong Dong, Xiaochun Li, Will Sawin

We prove that, under certain conditions on the function pair $φ_{1}$ and $φ_{2}$ , bilinear average $p^{- 1} \sum_{y \in F_{p}} f_{1} (x + φ_{1} (y)) f_{2} (x + φ_{2} (y))$ along curve $(φ_{1}, φ_{2})$ …

math.CA2015★ 5 cited

$L^{p}$ -estimates of maximal function related to Schrödinger Equation in $R^{2}$

Xiumin Du, Xiaochun Li

Using Guth's polynomial partitioning method, we obtain $L^{p}$ estimates for the maximal function associated to the solution of Schrödinger equation in $R^{2}$ . The $L^{p}$ estim…

math.CA2013★ 5 cited

Uniform estimates for bilinear Hilbert transform and bilinear maximal functions associated to polynomials

Xiaochun Li, Lechao Xiao

We study the bilinear Hilbert transform and bilinear maximal functions associated to polynomial curves and obtain uniform $L^{r}$ estimates for $r > \frac{d - 1}{d}$ and this index is sh…

Two bipolynomial Roth theorems in R