ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE 被引量：4

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

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摘要 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. 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.

作者张艳慧邓冠铁高洁欣

机构地区 Department of Mathematics School of Mathematical Sciences Department of Mathematics

出处《Acta Mathematica Scientia》 SCIE CSCD 2012年第4期1487-1494,共8页 数学物理学报（B辑英文版）

基金 Project supported by the Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB201008257) Scientific Research Common Program of Beijing Municipal Commission of Education (KM200810011005) PHR (IHLB 201102) research grant of University of Macao MYRG142(Y1-L2)-FST111-KKI

关键词 harmonic function Carleman＇s formula Nevanlinna＇s representation for halfsphere lower bound harmonic function Carleman＇s formula Nevanlinna＇s representation for halfsphere lower bound

分类号 O174.3 [理学—基础数学] O347.41 [理学—固体力学]

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