Resumen de Radial growth of harmonic functions in the unit ball

Kjersti Solberg Eikrem, Eugenia Malinnikova

• Let Ψv be the class of harmonic functions in the unit disk or unit ball in Rm which admit a radial majorant v(r). We prove that a function in Ψv 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.