MULTIPLIERS AND CHARACTERIZATION OF THE DUAL OF NEVANLINNA-TYPE SPACES

Pub Date : 2023-09-07 DOI:10.1017/nmj.2023.24

Mieczysław Mastyło, Bartosz Staniów

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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

. As a by-product, we prove a representation of continuous linear functionals on

$N_\varphi $

.

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nevanlinna型空间的乘数和对偶的表征

研究了由Rudin意义上的强凸函数$\varphi $生成的复平面圆盘上解析函数的nevanlinna型空间$N_\varphi $。对于一类特殊的强凸函数，我们给出了函数在$N_\varphi $中泰勒系数增长的渐近界，并利用这些渐近界刻画了从$N_\varphi $到$H^p$的Hardy空间的系数乘子。作为副产品，我们证明了连续线性泛函在$N_\varphi $上的表示。

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