4 papers · 1 filter
Refined restriction estimate for eigenfunctions on Riemannian surfaces
Chuanwei Gao, Changxing Miao, Yakun Xi
We refine the restriction estimates for Laplace eigenfunctions on a Riemannian surface, originally established by Burq, Gérard, and Tzvetkov. First, we establish estimates f…
Hörmander oscillatory integral operators: a revisit
Chuanwei Gao, Zhong Gao, Changxing Miao
In this paper, we present new proofs for both the sharp estimate and the decoupling theorem for the Hörmander oscillatory integral operator. The sharp estimate was pre…
Decoupling for finite type phases in higher dimensions
Chuanwei Gao, Zhuoran Li, Tengfei Zhao +1
In this paper, we establish an decoupling inequality for the hypersurface \[\Big\{(ξ_1,...,ξ_{n-1},ξ_1^m+...+ξ_{n-1}^m): (ξ_1,...,ξ_{n-1}) \in [0,1]^{n-1}\Big\}\]ass…
Square function inequality for oscillatory integral operators satisfying homogeneous Carleson-Sjölin type conditions
Chuanwei Gao, Changxing Miao, Jianwei-Urbain Yang
In this paper, we establish an improved variable coefficient version of square function inequality, by which the local smoothing estimate for the Fourier in…