Smoothness of subharmonic functions

The smoothness of functions subharmonic in a domain $D\subset\mathbf R^n$, $n\geqslant 2$, is studied. The method for studying smoothness is based on the Riesz theorem on representation of a subharmonic function as the sum of a harmonic function and the potential $U^\mu(x)$ with respect to some Borel measure $\mu$.