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Comptes Rendus Mathématique
Volume 352, n° 11
pages 889-893 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.019
Received : 6 August 2014 ;  accepted : 23 September 2014
On the higher dimensional harmonic analog of the Levinson   theorem
Sur l'analogue harmonique du théorème   de Levinson pour plusieurs dimensions
 

Alexander Logunov
 Saint Petersburg State University, Chebyshev Laboratory, 14th Line 29B, Vasilyevsky Island, St. Petersburg, Russia 

Abstract

Let M :   be a decreasing function such that  . Consider the set   of all functions u harmonic in   and satisfying  . We prove that   is a normal family in P .

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Résumé

Soit   une fonction décroissante telle que  . Considérons l'ensemble   de toutes les fonctions u qui sont harmoniques dans   et satisfont  . On montre que   est une famille normale dans P .

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