Sajin Vincent A W

On the Boundedness of Hypersingular Integrals Along Certain Radial Hypersurfaces

We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form $Γ(t)=(t,φ(t)), t\in\R{n}$. When $φ$ satisfies suitable curvature and monotonicity conditions, we prove $L^p(\R{n+1})$ boundedness of the operator, where the range of $p$ depends on the hypersingularity of the operator. We also establish certain Sobolev estimates of the operator under consideration.