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

Abstract

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