Estimates for some potential type operators whose kernels have singularities on spheres

Multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in $\mathbb R^n$ are studied on Hardy spaces $H^p$, $0<p<\infty$. Necessary and sufficient conditions are obtained for such operators to be bounded from $H^p$ into the Holder space $\Lambda_s$, from $H^p$ into the Sobolev space $L_k^\infty$, and from BMO into $\Lambda_s$.