A rough hypersingular integral operator with an oscillating factor

We study certain hypersingular integrals TΩ,α,βf defined on all test functions f∈S(Rn), where the kernel of the operator TΩ,α,β has a strong singularity |y|−n−α (α>0) at the origin, an oscillating factor ei|y|−β (β>0) and a distribution Ω∈Hr(Sn−1), 02α>0.