ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional...

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Veröffentlicht in:Acta mathematica scientia 2012-07, Vol.32 (4), p.1487-1494
1. Verfasser: 张艳慧 邓冠铁 高洁欣
Format: Artikel
Sprache:eng
Schlagworte:
31B05
35J05
Carleman's formula
harmonic function
lower bound
Nevanlinna's representation for half sphere
中国科学院
半平面
半空间
定理
研究生院
调和函数
高维
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Beschreibung
Zusammenfassung:The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(12)60117-9