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

doi:10.1016/S0252-9602(12)60117-9

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1487-1494.doi: 10.1016/S0252-9602(12)60117-9

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

张艳慧¹|邓冠铁^2*|高洁欣³

1.Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China|2.School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China|3.Department of Mathematics, Faculty of Science and Technology, University of Macau, China

收稿日期:2010-09-10 修回日期:2010-10-26 出版日期:2012-07-20 发布日期:2012-07-20
通讯作者: 邓冠铁,denggt@bnu.edu.cn E-mail:zhangyanhui@th.btbu.edu.cn; denggt@bnu.edu.cn; kikou@umac.mo
基金资助:
Project supported by the Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB201008257) and Scientific Research Common Program of Beijing Municipal Commission of Education (KM200810011005) and PHR (IHLB 201102) and research grant of University of Macau MYRG142(Y1-L2)-FST111-KKI.

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

ZHANG Yan-Hui¹, DENG Guan-Tie^2*, GAO Jie-Xin³

1.Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China|2.School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China|3.Department of Mathematics, Faculty of Science and Technology, University of Macau, China

Received:2010-09-10 Revised:2010-10-26 Online:2012-07-20 Published:2012-07-20
Contact: DENG Guan-Tie,denggt@bnu.edu.cn E-mail:zhangyanhui@th.btbu.edu.cn; denggt@bnu.edu.cn; kikou@umac.mo
Supported by:
Project supported by the Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB201008257) and Scientific Research Common Program of Beijing Municipal Commission of Education (KM200810011005) and PHR (IHLB 201102) and research grant of University of Macau MYRG142(Y1-L2)-FST111-KKI.

摘要/Abstract

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 H¨ormander's theorem.

关键词: harmonic function, Carlemans formula, Nevanlinnas representation for half sphere, lower bound

Abstract:

Key words: harmonic function, Carlemans formula, Nevanlinnas representation for half sphere, lower bound

中图分类号:

31B05

张艳慧, 邓冠铁, 高洁欣. ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE[J]. 数学物理学报(英文版), 2012, 32(4): 1487-1494.

ZHANG Yan-Hui, DENG Guan-Tie, GAO Jie-Xin. ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1487-1494.

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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

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