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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.
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참고문헌 (6)
참고문헌 신청
P. Ahern / 1993 / An Invariant Volume-Mean-Value Property / Journal of Functional Analysis 111(2):380~397
L. V. Ahlfors / 1981 / M¨obius Transformations in Several Dimensions, Ordway Professorship Lectures in Mathematics / University of Minnesota, School of Mathematics
Heinz Leutwiler / 1987 / Best constants in the Harnack inequality for the Weinstein equation / Aequationes Mathematicae 34(2-3):304~315
Congwen Liu / 2004 / Boundary regularity in the Dirichlet problem for the invariant Laplacians ∆γ on the unit real ball / Proceedings of the American Mathematical Society 132(11):3259~3268
Cong Wen Liu / 2003 / Invariant Mean-Value Property and M-Harmonicity in the Unit Ball of ℝ n / Acta Mathematica Sinica, English Series 19(1):187~200
L. V. Ahlfors / 1981 / M¨obius Transformations in Several Dimensions, Ordway Professorship Lectures in Mathematics / University of Minnesota, School of Mathematics
Heinz Leutwiler / 1987 / Best constants in the Harnack inequality for the Weinstein equation / Aequationes Mathematicae 34(2-3):304~315
Congwen Liu / 2004 / Boundary regularity in the Dirichlet problem for the invariant Laplacians ∆γ on the unit real ball / Proceedings of the American Mathematical Society 132(11):3259~3268
Cong Wen Liu / 2003 / Invariant Mean-Value Property and M-Harmonicity in the Unit Ball of ℝ n / Acta Mathematica Sinica, English Series 19(1):187~200
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