On the higher dimensional harmonic analog of the Levinson log log theorem

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Abstract

Let M: (0, 1)→[. e, +. ∞) be a decreasing function such that {intercalate}01log log M(y)dy<+∞. Consider the set HM of all functions u harmonic in P:={(x,y):x∈n-1,y∈,|x|<1,|y|<1} and satisfying |. u(. x, y)|. ≤. M(|. y|). We prove that HM is a normal family in P.

Original languageEnglish (US)
Pages (from-to)889-893
Number of pages5
JournalComptes Rendus Mathematique
Volume352
Issue number11
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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