Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (4): 1487-1494.doi: 10.1016/S0252-9602(12)60117-9

• Articles • Previous Articles     Next Articles

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

 ZHANG Yan-Hui1, DENG Guan-Tie2*, GAO Jie-Xin3   

  1. 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.

Abstract:

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.

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

CLC Number: 

  • 31B05
Trendmd