Properties of Bounded Holomorphic Functions: A Survey

Author:

Jarnicki Marek,Pflug PeterORCID

Abstract

AbstractWe discuss interrelations between$$\mathcal {H}^\infty $$H-convex domains and$$\mathcal {H}^\infty $$H-domains of holomorphy for various classes of domains in$$\mathbb {C}^{n}$$Cn.

Funder

Carl von Ossietzky Universität Oldenburg

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology

Reference19 articles.

1. Ahern, P.R., Schneider, R.: Isometries of $$\cal{H}^\infty $$. Duke Math. J. 42, 321–326 (1975)

2. Backlund, U.: A bounded domain of holomorphy for which the volume of the $$\cal{H}^\infty $$ -envelope of holomorphy is infinite. Complex Variables Theory Appl. 23, 151–155 (1993)

3. Backlund, U.: Comparison of certain $$\cal{H}^\infty $$-domains of holomorphy. Trans. Am. Math. Soc. 347, 2917–2926 (1995)

4. Backlund, U., Fällström, A.: A pseudoconvex domain with nonschlicht $$\cal{H}^\infty $$-envelope, In Geometrical and algebraic aspects in several complex variables, Cetraro (1989). Seminars and conferences, Editel (1991)

5. Catlin, D.: Boundary behavior of holomorphic functions on pseudoconvex domains. J. Differ. Geom. 15, 605–625 (1980)

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