沿一类变非凸曲线的Hilbert变换的L^(2)有界性  

L^(2) Boundedness for Hilbert Transforms Along a Class of Variable Nonconvex Curves

作　　者：王先彪[1] 于海峡 WANG Xianbiao;YU Haixia(School of Electromechanical Engineering,Guangzhou Railway Polytechnic,Guangzhou,Guangdong,510430,P.R.China;School of Mathematics,Sun Yat-sen University,Guangzhou,Guangdong,510275,P.R.China;Department of Mathematics,Shantou University,Shantou,Guangdong,515063,P.R.China)

机构地区：[1]广州铁路职业技术学院机电工程学院,广东广州510430 [2]中山大学数学学院,广东广州510275 [3]汕头大学数学系,广东汕头515063

出　　处：《数学进展》2023年第1期152-162,共11页Advances in Mathematics（China）

基　　金：supported by NSFC(No.12201378);STU Scientific Research Foundation for Talents(No.NTF21038)。

摘　　要：在u:R→R是一个可测函数,P:R→R是一个实多项式和γ满足一些合适的光滑性和曲率条件的前提下,本文证明了沿变曲线(t,u(x_(1))P(γ(t)))的Hilbert变换在L^(2)空间中的有界性.We prove that the Hilbert transforms along the variable plane curves(t,u(x_(1))P(γ(t))),is bounded on L^(2)(R^(2)),under the assumption that u:R→R is a measurable function,P:R→R is a real polynomial and γ satisfies some suitable smoothness and curvature conditions.

关 键 词：HILBERT变换 变曲线 Carleson型算子 驻相法 

分 类 号：O174.2[理学—数学]