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We use sphericalization to study the Dirichlet problem, Perron solutions andboundary regularity for p-harmonic functions on unbounded sets in Ahlforsregular metric spaces. Boundary regularity for the point at infinity is givenspecial attention. In particular, we allow for several "approach directions"towards infinity and take into account the massiveness of their complements. In2005, Llorente-Manfredi-Wu showed that the p-harmonic measure on the upper halfspace $R^n_+, n \ge 2$, is not subadditive on null sets when $p \neq 2$. Usingtheir result and spherical inversion, we create similar bounded examples in theunit ball $B \subset R^n$ showing that the n-harmonic measure is notsubadditive on null sets when $n \ge 3$, and neither are the p-harmonicmeasures in $B$ generated by certain weights depending on $p\neq 2$ and $n \ge2$.

Sphericalization and p-harmonic functions on unbounded domains in Ahlfors regular metric spaces