3 citations · 6 across the 11 of their papers we have counts for
5 papers · 1 filter
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…
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…
A polynomial Roth theorem for corners in and a related bilinear singular integral operator
Xuezhi Chen, Jingwei Guo
We prove a quantitative Roth-type theorem for polynomial corners in . Let and be two linearly independent polynomials with zero constant term. We show tha…
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…
Two bipolynomial Roth theorems in
Xuezhi Chen, Jingwei Guo, Xiaochun Li
We give two Roth theorems, related to the nonlinear configuration , , involving two polynomials, for sets in of positive density and of fractio…