Radial growth of harmonic functions in the unit ball - Eikrem, Kjersti Solberg; Malinnikova, Eugenia (MATHEMATICA SCANDINAVICA, 2012)
Let Ψ_v be the class of harmonic functions in the unit disk or unit ball in R^m which admit a radial majorant v(r). We prove that a function in Ψ_v may grow or decay as fast as v only along a set of radii of measure zero. For the case when v fulfills a doubling condition, we give precise estimates of these exceptional sets in terms of Hausdorff measures.