On n-circled $ℋ^{∞}$-domains of holomorphy

ArticleOriginal scientific text

Title

Authors ¹, ²

Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Fachbereich Mathematik, Carl Von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany

We present various characterizations of n-circled domains of holomorphy

G \subset ℂ^{n}

with respect to some subspaces of

ℋ^{\infty} (G)

.

n-circled domain of holomorphy

[Fer] J.-P. Ferrier, Spectral Theory and Complex Analysis, North-Holland, Amsterdam, 1973.
[Fu] S. Fu, On completeness of invariant metrics of Reinhardt domains, Arch. Math. (Basel) 63 (1994), 166-172.
[Jar-Pfl 1] M. Jarnicki and P. Pflug, Existence domains of holomorphic functions of restricted growth, Trans. Amer. Math. Soc. 304 (1987), 385-404.
[Jar-Pfl 2] M. Jarnicki and P. Pflug, On balanced L²-domains of holomorphy, Ann. Polon. Math. 63 (1996), 101-102.
[Pfl] P. Pflug, Über polynomiale Funktionen auf Holomorphiegebieten, Math. Z. 139 (1974), 133-139.
[Sib] N. Sibony, Prolongement de fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230.
[Sic 1] J. Siciak, Circled domains of holomorphy of type $ℋ^{\infty}$ , Bull. Soc. Sci. Lett. Łódź 34 (1984), 1-20.
[Sic 2] J. Siciak, Balanced domains of holomorphy of type $H^{\infty}$ , Mat. Vesnik 37 (1985), 134-144.