Radial growth of harmonic functions in the unit ball

• Autores: Kjersti Solberg Eikrem, Eugenia Malinnikova
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 110, Nº 2, 2012, págs. 273-296
• Idioma: inglés
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• Resumen

  • 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.