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On the minimum of harmonic functions

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Abstract

Letu be a function harmonic in the unit disc or in the plane, and letu(z)≤M(|z|) for a majorantM. We formulate conditions onM that guarantee thatu(z)≥−(1+o(1))M(|z|) for |z|→1 in the disc and for |z|→∞ in the plane.

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Authors and Affiliations

  1. Department of Mathematics, University of Bordeaux I, 351, Cours de la Libération, 33405, Talence, France

    Alexander Borichev

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  1. Alexander Borichev
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Correspondence to Alexander Borichev.

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Borichev, A. On the minimum of harmonic functions. J. Anal. Math. 89, 199–212 (2003). https://doi.org/10.1007/BF02893081

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  • DOI: https://doi.org/10.1007/BF02893081

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