Estimates for some potential-type operators with oscillating symbols

In the framework of Hardy spaces $H^p$, we study multidimensional potential-type operators whose kernels have singularities on the unit sphere. Necessary and sufficient conditions are obtained for such operators to be bounded from $H^p$ to $H^q$, from $BMO$ to $L^\infty$, from $L^1$ to $H^1$ or from $BMO$ to $BMO$.