Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-30T20:17:47.506Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)