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Banach space properties of strongly tight uniform algebras

Scott Saccone (1995)

Studia Mathematica

We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K), then A and...

Boundary behaviour of invariant distances and complex geodesics

Marco Abate (1986)

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

In questa Nota viene studiato il comportamento al bordo delle distanze di Carathéodory e Kobayashi in domini fortemente pseudoconvessi di classe 𝐂 2 . Come applicazione si dimostra che ogni geodetica complessa in tali domini è estendibile al bordo di classe 𝐂 0 , 1 2 .

B-regularity of certain domains in ℂⁿ

Nguyen Quang Dieu, Nguyen Thac Dung, Dau Hoang Hung (2005)

Annales Polonici Mathematici

We study the B-regularity of some classes of domains in ℂⁿ. The results include a complete characterization of B-regularity in the class of Reinhardt domains, we also give some sufficient conditions for Hartogs domains to be B-regular. The last result yields sufficient conditions for preservation of B-regularity under holomorphic mappings.

Classes de Nevanlinna sur une intersection d'ouverts strictement pseudoconvexes.

Chantal Menini (1995)

Publicacions Matemàtiques

On a finite intersection of strictly pseudoconvex domains we define two kinds of natural Nevanlinna classes in order to take the growth of the functions near the sides or the edges into account. We give a sufficient Blaschke type condition on an analytic set for being the zero set of a function in a given Nevanlinna class. On the other hand we show that the usual Blaschke condition is not necessary here.

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