12 citations · 63 across the 29 of their papers we have counts for
14 papers · 1 filter
Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters
Shengwen Gan, Cheng Zhang, Zhifei Zhu
We prove sharp -linear estimates for Carleson--Sjölin oscillatory integral operators with arbitrary separated frequency scales for all and . The…
Restriction estimates for toral eigenfunctions and lattice points in spherical regions
Cheng Zhang, Zhifei Zhu
We establish new restriction estimates for toral eigenfunctions. These estimates are sharp in certain cases, and thus prove a conjecture of Huang-Zhang for smooth submanifold…
Sharp local estimates for the Hermite eigenfunctions
Xing Wang, Cheng Zhang
We investigate the concentration of eigenfunctions for the Hermite operator in by establishing local bounds over the compact sets with arbitrary d…
Sharp estimates and size of nodal sets for generalized Steklov eigenfunctions
Xiaoqi Huang, Yannick Sire, Xing Wang +1
We prove sharp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their norms on the boundary. We prove it by establishing bo…
Sharp Pointwise Weyl Laws for Schrödinger Operators with Singular Potentials on Flat Tori
Xiaoqi Huang, Cheng Zhang
The Weyl law of the Laplacian on the flat torus is concerning the number of eigenvalues , which is equivalent to counting the lattice points inside the ball…
Pointwise Weyl Laws for Schrödinger operators with singular potentials
Xiaoqi Huang, Cheng Zhang
We consider the Schrödinger operators with singular potentials on general -dimensional Riemannian manifolds and study whether various forms of pointwise Weyl la…
eigenfunction bounds for fractional Schrödinger operators on manifolds
Xiaoqi Huang, Yannick Sire, Cheng Zhang
This paper is dedicated to bounds on eigenfunctions of a Schödinger-type operator on closed Riemannian manifolds for critically singular potentials . The…
Interior estimates for the eigenfunctions of the fractional Laplacian on a bounded Euclidean domain
Xiaoqi Huang, Yannick Sire, Cheng Zhang
This paper is devoted to interior, i.e. away from the boundary, estimates for eigenfunctions of the fractional Laplacian in an Euclidean domain of .
Restriction of toral eigenfunctions to totally geodesic submanifolds
Xiaoqi Huang, Cheng Zhang
We estimate the norm of the restriction to a totally geodesic submanifold of the eigenfunctions of the Laplace-Beltrami operator on the standard flat torus , $d…
An Endpoint Version of Uniform Sobolev Inequalities
Tianyi Ren, Yakun Xi, Cheng Zhang
We prove an endpoint version of the uniform Sobolev inequalities in Kenig-Ruiz-Sogge [8]. It was known that strong type inequalities no longer hold at the endpoints; however, we sh…
Improved critical eigenfunction restriction estimates on Riemannian manifolds with constant negative curvature
Cheng Zhang
We show that one can obtain logarithmic improvements of geodesic restriction estimates for eigenfunctions on 3-dimensional compact Riemannian manifolds with constant negative…
Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet Theorem
Christopher D. Sogge, Yakun Xi, Cheng Zhang
We use the Gauss-Bonnet theorem and the triangle comparison theorems of Rauch and Toponogov to show that on compact Riemann surfaces of negative curvature period integrals of eigen…
Improved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature
Yakun Xi, Cheng Zhang
We show that one can obtain improved geodesic restriction estimates for eigenfunctions on compact Riemannian surfaces with nonpositive curvature. We achieve this by adapting…
A new kind of functional differential equations
De-Xing Kong, Cheng Zhang
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore…