arXiv subjects

Jianwei-Urbain Yang

Publications and source records attributed to Jianwei-Urbain Yang.

2 recordsLinked to original sources

arXiv2024

Square function inequality for oscillatory integral operators satisfying homogeneous Carleson-Sjölin type conditions

In this paper, we establish an improved variable coefficient version of square function inequality, by which the local smoothing estimate $L^p_α\rightarrow L^p$ for the Fourier integral operators satisfying cinematic curvature condition is further improved. In particular, we establish almost sharp results for $2<p\leq 3$ and push forward the estimate for the critical point $p=4$. As a consequence, the local smoothing estimate for the wave equation on the manifold is refined. We generalize the results in \cite{LeVa12, Le18P} to its variable coefficient counterpart. The main ingredients in the argument includes multilinear oscillatory integral estimate \cite{BCT06} and decoupling inequality \cite{BelHicSog18P}.

math.AP↗

arXiv2019

Improved variable coefficient square functions and local smoothing of Fourier integral operators

We establish certain square function estimates for a class of oscillatory integral operators with homogeneous phase functions. These results are employed to deduce a refinement of a previous result of Mockenhaupt Seeger and Sogge \cite{MSS-jams} on the local smoothing property for Fourier integral operators, which arise naturally in the study of wave equations on compact Riemannian manifolds. The proof is an adaptation of the bilinear approach of Tao and Vargas \cite{Tao-Vargas-II}, %as well as Garrigós and Seeger \cite{GaSe09}, and based on bilinear oscillatory integral estimates of Lee \cite{Lee-JFA}.

math.AP↗