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ArticleOriginal scientific text

Title

Linearly invariant families of holomorphic functions in the unit polydisc

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Maria Curie-Skłodowska University, PL-20-031 Lublin, Poland
  2. Department of Mathematics, University of Petrozavodsk, Petrozavodsk, Russia

Abstract

In this paper we extend the definition of the linearly invariant family and the definition of the universal linearly invariant family to higher dimensional case. We characterize these classes and give some of their properties. We also give a relationship of these families with the Bloch space.

Bibliography

  1. Ch. Pommerenke, Linear-invariante Familien analytischer Funktionen, Math. Ann., 155 (1964), 108-154.
  2. J. Godula, V. Starkov, Applications of ideas of Möbius invariance to obtaining equivalent definitions of Bloch functions, Annales Univ. Mariae Curia-Skłodowska 49 (1996), 41-58.
  3. J. Godula, V. Starkov, Equivalent definitions of universal linearly-invariant familie, Materiały XI Konferencji Szkoleniowej z Teorii Zagadnień Ekstremalnych, Łódź, 1990, 34-38.
  4. R.M. Timoney, Bloch functions in several complex variables, I, Bull. London Math. Soc., 12 (1980), 241-267.
Banach Center Publications
1996/37/1
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Pages:
115-127
Main language of publication
English
Published
1996
Exact and natural sciences