The Behavior, onḂ0,11, of an Oscillatory Integral with Polynomial Phase Function

AbstractWe study the convolution oscillatory singular integral operatorTf=p.v.Ω∗f, with Ω(x)=eiq(x)K(x), whereqis a real-valued polynomial of a real variable, of degreed≥2, andKis a Calderón–Zygmund-type kernel. We prove that this operator extends to an operator that maps the Besov spaceḂ0,11into the Hardy-type spaceH10