粗糙Carleson型极大算子的Lp 有界性

Stein and Wainger have proved that Carleson type maximal operators is Lp bounded, where the phase function P(y) is polynomial without linear term and singular kernel K is smooth. In this artical, authors consider another kind of Carleson type maximal operators, where the phase function is P(|y|), P(t) is a polynomial on R without linear term, K(y)=Ω(y)/|y|n, Ω∈H1(Sn-1). They obtain the Lp boundedness for this kind of Carleson type maximal operators by Stein-Wainger's TT* argument and Calderon-Zygmund's rotation method.