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PROPAGATION OF SMALLNESS FOR HARMONIC AND ANALYTIC FUNCTIONS IN ARBITRARY DOMAINS
Published online by Cambridge University Press: 01 November 1999
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).
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- © The London Mathematical Society 1999
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