Abstract: In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygrnund kernel, which had been studied by Ricci and Stein in[6], and extend their result. We get that T is bounded on L^p(Rⁿ)(1<p<∞) when-1<μ<αd(1/2)-|(1/p)-(1/2)|).

Key words: oscillatory singular integral operator, Calder6n-Zygmund kernel, boundedness