We study certain hypersingular integrals F-Omega,F-alpha,F-beta f defined on all test functions f is an element of P(R-n), where the kernel of the operator F-Omega,F-alpha,F-beta has a strong singularity vertical bar y vertical bar(-n-alpha) (alpha > 0) at the origin, an oscillating factor e(i vertical bar y vertical bar-beta) (beta > 0) and a distribution Omega is an element of H-r(Sn-1), 0 < r < 1. We show that F-Omega,F-alpha,F-beta extends to a bounded linear operator from the Sobolev space L-gamma(P) boolean AND L-P to the Lebesgue space L-P for beta/(beta - alpha) < p < beta/alpha, if y ...
