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.
作者
王先彪
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)
出处
《数学进展》
CSCD
北大核心
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)。
