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

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 Hormander's theorem.
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