Acta mathematica scientia, Series B >
ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE
Received date: 2010-09-10
Revised date: 2010-10-26
Online published: 2012-07-20
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.
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.
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 . DOI: 10.1016/S0252-9602(12)60117-9
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