Displaying similar documents to “Hua-harmonic functions on symmetric type two Siegel domains”

The Hua system on irreducible Hermitian symmetric spaces of nontube type

Dariusz Buraczewski (2004)

Annales de l’institut Fourier

Similarity:

Let G / K be an irreducible Hermitian symmetric space of noncompact type. We study a G - invariant system of differential operators on G / K called the Hua system. It was proved by K. Johnson and A. Korányi that if G / K is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube...

Polynomially growing pluriharmonic functions on Siegel domains

Monika Gilżyńska (2007)

Colloquium Mathematicae

Similarity:

Let 𝓓 be a symmetric type two Siegel domain over the cone of positive definite Hermitian matrices and let N(Φ)S be a solvable Lie group acting simply transitively on 𝓓. We characterize polynomially growing pluriharmonic functions on 𝓓 by means of three N(Φ)S-invariant second order elliptic degenerate operators.

Pluriharmonic functions on symmetric tube domains with BMO boundary values

Ewa Damek, Jacek Dziubański, Andrzej Hulanicki, Jose L. Torrea (2002)

Colloquium Mathematicae

Similarity:

Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered. ...