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

Alexander Logunov

doi:10.1016/j.crma.2014.09.019

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

Alexander Logunov

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let M: (0, 1)→[. e, +. ∞) be a decreasing function such that {intercalate}₀¹log log M(y)dy<+∞. Consider the set H_M 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 H_M is a normal family in P.

Original language	English (US)
Pages (from-to)	889-893
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	352
Issue number	11
DOIs	https://doi.org/10.1016/j.crma.2014.09.019
State	Published - 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2014.09.019

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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.",

author = "Alexander Logunov",

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AB - 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.

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JO - Comptes Rendus Mathematique

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IS - 11

ER -

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

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