2006
DOI: 10.1007/s00208-006-0776-1
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Asymptotic expansions and Hua-harmonic functions on bounded homogeneous domains

Abstract: Let D be a homogeneous Siegel domain of type II. We prove that every bounded Hua-harmonic function F on D is pluriharmonic. The proof is based on asymptotic expansion of F .

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Cited by 2 publications
(3 citation statements)
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“…One can show (using e.g. [23,Theorem 4]) that every continuous bounded function on a Lipschitz domain U , which is harmonic for ∆ η , η > 0, has a limit at the boundary of U . All this leads us to the following modified Dirichlet problem:…”
Section: General Resultsmentioning
confidence: 99%
“…One can show (using e.g. [23,Theorem 4]) that every continuous bounded function on a Lipschitz domain U , which is harmonic for ∆ η , η > 0, has a limit at the boundary of U . All this leads us to the following modified Dirichlet problem:…”
Section: General Resultsmentioning
confidence: 99%
“…Let U be an algebra with an involution . As in [19], we define the subspace of "Hermitian matrices" in U,…”
Section: Definition 21mentioning
confidence: 99%
“…Since the mapping H s → ss ∈ is one-to-one, the group H acts simply transitively on by (2.3). Hence, by homogeneity, one can write = H • e, where we use the notation π(t)e = t • e for all t ∈ H. As it is mentioned in [19], we have the factorization…”
Section: Proposition 25 ([20 Proposition 1 Page 384])mentioning
confidence: 99%