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PROPAGATION OF SMALLNESS FOR HARMONIC AND ANALYTIC FUNCTIONS IN ARBITRARY DOMAINS

Published online by Cambridge University Press:  01 November 1999

NORAIR ARAKELIAN  and
HENRIK SHAHGHOLIAN
NORAIR ARAKELIAN
Affiliation:
Institute of Mathematics, National Academy of Sciences of Armenia, Marshal Bagramian Street, 24 B, 375019 Yerevan, Armenia
HENRIK SHAHGHOLIAN
Affiliation:
Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
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Abstract

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).

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 6 , November 1999 , pp. 671 - 678
Copyright
© The London Mathematical Society 1999

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