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 ${\mathsf R}^m$ 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.