L~2 Boundedness Of The Hilbert Transform Along Some Convex Flat Curves

In this paper,the author introduces the main research achievements during study-ing for master's degree.In this paper,we mainly consider the Boundedness of Hilbert transform along a class of flat convex curves:The author difines the first special curve,Then,The author mainly use the Plancherel theorem and through Van Der Corput lemma and oscillatory integral operator to get the necessary condition for H? bounded on L2 The author difines the second special curve.Use the same method,We can get the necessary condition for H? bounded on L~2.