  $(L_p, L_q)$ estimates are obtained for oscillatory potentials
$(K^\alphaf)(x)=\int\limits_{R^n}\frac{\exp(i|y|)}{|y|^{n-\alpha}}f(x-y)dy$,
  $0<\alpha<n$, $n\geq 2$, whose symbol has a singularity on the unit sphere.
These potentials are natural modifications of the celebrated Bochner-Riesz
operator and Helmholtz potential arising in Fourier analysis and PDE. For some
values of $\alpha$, determination of the corresponding pairs $(L_p, L_q)$
represents an open problem. The range of $\alpha$ for which the problem is open
is just the same as for the Bochner-Riesz means.
