PROPAGATION OF SMALLNESS FOR HARMONIC AND ANALYTIC FUNCTIONS IN ARBITRARY DOMAINS

PROPAGATION OF SMALLNESS FOR HARMONIC AND ANALYTIC FUNCTIONS IN ARBITRARY DOMAINS

In this paper the authors develop a new approach to the problem of ‘propagation of smallness’ for harmonic functions in arbitrary domains, in ℝn (n[ges ]2). The main result of this paper is a certain logarithmic-convexity relation for the L2-norms of harmonic functions. As a consequence, new kinds o...

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Veröffentlicht in:The Bulletin of the London Mathematical Society 1999-11, Vol.31 (6), p.671-678
Hauptverfasser: ARAKELIAN, NORAIR, SHAHGHOLIAN, HENRIK
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper the authors develop a new approach to the problem of ‘propagation of smallness’ for harmonic functions in arbitrary domains, in ℝn (n[ges ]2). The main result of this paper is a certain logarithmic-convexity relation for the L2-norms of harmonic functions. As a consequence, new kinds of uniqueness results for harmonic functions are obtained. The method works also for analytic functions in [Copf ], with Lp-norms (p>0).
ISSN:0024-6093
1469-2120
DOI:10.1112/S0024609399006268