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| In 2001, 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 use TT* method to generalize Stein and Wainger's result, that is, Carleson type maximal operators is weighted Lp bounded for 1<p<∞, where phase function P(y) is polynomial without linear terms, K(y)=Ω(y)/|y|n, Ω satisfies Lq-Dini condition, 1<q≤∞. |
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| Keywords:Fundamental Mathematics; Carleson type maximal operators; Singular integrals; TT* methods; Lq-Dini condition |
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