On the lower bound for a class of harmonic functions in the half space |
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| Authors: | Zhang Yanhui Deng Guantie Kou Kit Ian |
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| Institution: | 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 |
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| 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 Hörmander's theorem. |
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| Keywords: | harmonic function Carleman's formula Nevanlinna's representation for half sphere lower bound |
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