The Behavior, on B˙0, 1, of an Oscillatory Integral 1 with Polynomial Phase Function

We study the convolution oscillatory singular integral operator Tfsp.v. V) f, with V x.seiq x.K x., where q is a real-valued polynomial of a real variable, of degree dG2, and K is a Calder´on]Zygmund-type kernel. We prove that this operator extends to an operator that maps the Besov space B˙10, 1 into the Hardy-type space H01.