Pluriharmonic functions on symmetric tube domains with BMO boundary values

Ewa Damek; Jacek Dziubański; Andrzej Hulanicki; Jose L. Torrea

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Displaying similar documents to “Pluriharmonic functions on symmetric tube domains with BMO boundary values”

Hua-harmonic functions on symmetric type two Siegel domains

Dariusz Buraczewski, Ewa Damek (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study a natural system of second order differential operators on a symmetric Siegel domain $D$ that is invariant under the action of biholomorphic transformations. If $D$ is of type two, the space of real valued solutions coincides with pluriharmonic functions. We show the main idea of the proof and give a survey of previous results.

Polynomially growing pluriharmonic functions on Siegel domains

Monika Gilżyńska (2007)

Colloquium Mathematicae

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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.

Invariant inner product in spaces of holomorphic functions on bounded symmetric domains.

Arazy, Jonathan, Upmeier, Harald (1997)

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Nonfactorization theorems for Hardy and Bergman spaces on bounded symmetric domains

Tomasz Wolniewicz (1987)

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Besov spaces on bounded symmetric domains.

Jevtić, Miroljub (1997)

Matematichki Vesnik

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The Hua system on irreducible Hermitian symmetric spaces of nontube type

Dariusz Buraczewski (2004)

Annales de l’institut Fourier

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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...

Effective formulas for invariant functions - case of elementary Reinhardt domains

Peter Pflug, Włodzimierz Zwonek (1998)

Annales Polonici Mathematici

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We find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.