Removable singularities for $n$-harmonic functions and Hardy classes in polydiscs

Abstract:

Let $\phi$ be any strongly convex function. For an open subset $G$ of a polydisc ${U^n}$ the Hardy class ${H_\phi }\left ( G \right )$ is the set of analytic functions $f$ on $G$ for which $\phi \circ \log \left | f \right |$ has an $n$-harmonic majorant. It is shown that ${H_\phi }\left ( {{U^n} \setminus E} \right ) = {H_\phi }\left ( {{U^n}} \right )$ for any relatively closed $n$-negligible subset $E$ of ${U^n}$.