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MULTIPLIERS AND CHARACTERIZATION OF THE DUAL OF NEVANLINNA-TYPE SPACES

Part of: Analytic spaces Linear function spaces and their duals Spaces and algebras of analytic functions

Published online by Cambridge University Press:  07 September 2023

MIECZYSŁAW MASTYŁO Open the ORCID record for MIECZYSŁAW MASTYŁO [Opens in a new window]  and
BARTOSZ STANIÓW Open the ORCID record for BARTOSZ STANIÓW [Opens in a new window]
MIECZYSŁAW MASTYŁO*
Affiliation:
Faculty of Mathematics and Computer Science Adam Mickiewicz University Uniwersytetu Poznańskiego 4 61-614 Poznań Poland
BARTOSZ STANIÓW
Affiliation:
Faculty of Mathematics and Computer Science Adam Mickiewicz University Uniwersytetu Poznańskiego 4 61-614 Poznań Poland bs21276@amu.edu.pl
*
e-mail: mieczyslaw.mastylo@amu.edu.pl
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Abstract

The Nevanlinna-type spaces $N_\varphi $ of analytic functions on the disk in the complex plane generated by strongly convex functions $\varphi $ in the sense of Rudin are studied. We show for some special class of strongly convex functions asymptotic bounds on the growth of the Taylor coefficients of a function in $N_\varphi $ and use these to characterize the coefficient multipliers from $N_\varphi $ into the Hardy spaces $H^p$ with $0<p\leqslant \infty $. As a by-product, we prove a representation of continuous linear functionals on $N_\varphi $.

MSC classification

Primary: 46E10: Topological linear spaces of continuous, differentiable or analytic functions 32C37: Duality theorems 30H15: Nevanlinna class and Smirnov class
Type
Article
Information
Nagoya Mathematical Journal , Volume 253 , March 2024 , pp. 216 - 240
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

M.M. was supported by the National Science Center, Poland, project no. 2019/33/B/ST1/00165.

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