沿平坦凸曲线Hilbert变换的L2有界性

L2 Boundedness of Hilbert Transform Along Convex Flat Curves

考虑一类平坦凸曲线的Hilbert变换Hγf(x)=p.v.∫+∞-∞f(x1-t,x2-γ(t))dt/t,(V)x:=(x1,x2)∈R2.对于平坦凸曲线,给出Hγ是L2有界的一些必要条件.

The authors consider the Hilbert transform along a convex flat curve in R^2:Hγf(x)=p.v.∫+∞-∞f(x1-t,x2-γ(t))dt/t,(V)x:=(x1,x2)∈R2.They give some necessary conditions such that H_γis bounded on L^2 for convex flat curves.