Radial growth of harmonic functions in the unit ball

Kjersti Solberg Eikrem, Eugenia Malinnikova


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.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15208


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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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