Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 897-904

ON THE SOLID HULLS OF THE NEVANLINNA AND SMIRNOV CLASSES

Marek Nawrocki

A. Mickiewicz University, Faculty of Mathematics and Computer Science
ul. Umultowska 87, 61-614 Poznan, Poland; nawrocki 'at' amu.edu.pl

Abstract. In the paper, the solid and positive solid hulls of the Nevanlinna class and the Smirnov class of the unit disc are described. The result is applied to find the best possible estimations of the Taylor coefficients and the multipliers from the Smirnov class into some large spaces of holomorphic functions. These results provide a much "softer" and easier way to obtain even stronger results on the multipiers and the mean growth of the Taylor coefficients proved by Yanagihara.

2010 Mathematics Subject Classification: Primary 30H15, 30H50, 46A16; Secondary 46E05.

Key words: Nevanlinna class, Smirnov class, Hardy algebra, Bergman algebra, Fréchet envelope, nuclear power series spaces.

Reference to this article: M. Nawrocki: On the solid hulls of the Nevanlinna and Smirnov classes. Ann. Acad. Sci. Fenn. Math. 39 (2014), 897-904.

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doi:10.5186/aasfm.2014.3953