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Holomorphic functions of fast growth on submanifolds of the domain

Piotr Jakóbczak (1998)

Annales Polonici Mathematici

We construct a function f holomorphic in a balanced domain D in N such that for every positive-dimensional subspace Π of N , and for every p with 1 ≤ p < ∞, f | Π D is not L p -integrable on Π ∩ D.

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

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.

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