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

{"title":"MULTIPLIERS AND CHARACTERIZATION OF THE DUAL OF NEVANLINNA-TYPE SPACES","authors":"Mieczysław Mastyło, Bartosz Staniów","doi":"10.1017/nmj.2023.24","DOIUrl":null,"url":null,"abstract":"\n\t The Nevanlinna-type spaces \n\t \n\t\t\n\t\t\n$N_\\varphi $\n\n\t \n\t of analytic functions on the disk in the complex plane generated by strongly convex functions \n\t \n\t\t\n\t\t\n$\\varphi $\n\n\t \n\t in the sense of Rudin are studied. We show for some special class of strongly convex functions asymptotic bounds on the growth of the Taylor coefficients of a function in \n\t \n\t\t\n\t\t\n$N_\\varphi $\n\n\t \n\t and use these to characterize the coefficient multipliers from \n\t \n\t\t\n\t\t\n$N_\\varphi $\n\n\t \n\t into the Hardy spaces \n\t \n\t\t\n\t\t\n$H^p$\n\n\t \n\t with \n\t \n\t\t\n\t\t\n$0<p\\leqslant \\infty $\n\n\t \n\t . As a by-product, we prove a representation of continuous linear functionals on \n\t \n\t\t\n\t\t\n$N_\\varphi $\n\n\t \n\t .","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/nmj.2023.24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

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

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

$N_\varphi $

查看原文

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文