Invariant mean value property and M-harmonicity on the half-space
Bull. Korean Math. Soc.
Published online July 16, 2020
Boo Rim Choe and Kyesook Nam
Korea university, Seoul National University
Abstract : It is well known that every invariant harmonic function on the
unit ball of the multi-dimensional complex space has the volume version of the invariant mean value
property. In 1993 Ahern, Flores and Rudin first observed that the validity of the converse depends on the dimension of the underlying complex space.
Later Lie and Shi obtained the analogues on the unit ball of multi-dimensional real space.
In this paper we obtain the half-space analogues of the results of Liu and Shi.
Keywords : Laplace-Beltrami operator, M-harmonic, Invariant mean value property, Invariant volume mean value property, Half-space
MSC numbers : 31B05, 31B10, 30D45, 30D55
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