Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664023 | Acta Mathematica Scientia | 2012 | 8 Pages |
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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