Radial growth of harmonic functions in the unit ball

  • Kjersti Solberg Eikrem
  • Eugenia Malinnikova

Abstract

Let $\Psi_v$ 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 $\Psi_v$ 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.
Published
2012-06-01
How to Cite
Eikrem, K. S., & Malinnikova, E. (2012). Radial growth of harmonic functions in the unit ball. MATHEMATICA SCANDINAVICA, 110(2), 273-296. https://doi.org/10.7146/math.scand.a-15208
Section
Articles