On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$
Under sufficiently general assumptions, we describe sets of entire functions $f$, sets of growing functions $λ$, and sets of complex-valued functions $H$ from $L^p [0, 2π]$, $p ∈ [1, + ∞]$, for which $$\left\{ {\frac{1}{{2\pi }}\int\limits_0^{2\pi } {|\log f(re^{i\theta } ) - \lambda (r)H(\theta )|^...
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| Date: | 1998 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4869 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511046120243200 |
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| author | Kalinets, R. Z. Koval’chuk, Yu. A. Калинець, Р. З. Ковальчук, Ю. А. |
| author_facet | Kalinets, R. Z. Koval’chuk, Yu. A. Калинець, Р. З. Ковальчук, Ю. А. |
| author_sort | Kalinets, R. Z. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:16:14Z |
| description | Under sufficiently general assumptions, we describe sets of entire functions $f$, sets of growing functions $λ$, and sets of complex-valued functions $H$ from $L^p [0, 2π]$, $p ∈ [1, + ∞]$, for which
$$\left\{ {\frac{1}{{2\pi }}\int\limits_0^{2\pi } {|\log f(re^{i\theta } ) - \lambda (r)H(\theta )|^p } d\theta } \right\}^{1/p} = o(\lambda (r)),r \to \infty.$$ |
| first_indexed | 2026-03-24T03:06:39Z |
| format | Article |
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| id | umjimathkievua-article-4869 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:06:39Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/da/a7680f63ad89a9f84d6437dd9d85f9da.pdf |
| spelling | umjimathkievua-article-48692020-03-18T21:16:14Z On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$ Про регулярність зростання модуля і аргумента цілої функції в $L^p [0, 2π]$-метриці Kalinets, R. Z. Koval’chuk, Yu. A. Калинець, Р. З. Ковальчук, Ю. А. Under sufficiently general assumptions, we describe sets of entire functions $f$, sets of growing functions $λ$, and sets of complex-valued functions $H$ from $L^p [0, 2π]$, $p ∈ [1, + ∞]$, for which $$\left\{ {\frac{1}{{2\pi }}\int\limits_0^{2\pi } {|\log f(re^{i\theta } ) - \lambda (r)H(\theta )|^p } d\theta } \right\}^{1/p} = o(\lambda (r)),r \to \infty.$$ При досить загальних припущепнях описуються множини цілих функцій $f$, зростаючих функцій $λ$, комплекснозпачпих функцій $H$ з $L^p [0, 2π]$, чисел $p ∈ [1, + ∞]$, для яких $$\left\{ {\frac{1}{{2\pi }}\int\limits_0^{2\pi } {|\log f(re^{i\theta } ) - \lambda (r)H(\theta )|^p } d\theta } \right\}^{1/p} = o(\lambda (r)),r \to \infty.$$ Institute of Mathematics, NAS of Ukraine 1998-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4869 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 7 (1998); 889-896 Український математичний журнал; Том 50 № 7 (1998); 889-896 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4869/6437 https://umj.imath.kiev.ua/index.php/umj/article/view/4869/6438 Copyright (c) 1998 Kalinets R. Z.; Koval’chuk Yu. A. |
| spellingShingle | Kalinets, R. Z. Koval’chuk, Yu. A. Калинець, Р. З. Ковальчук, Ю. А. On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$ |
| title | On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$ |
| title_alt | Про регулярність зростання модуля і аргумента цілої
функції в $L^p [0, 2π]$-метриці |
| title_full | On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$ |
| title_fullStr | On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$ |
| title_full_unstemmed | On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$ |
| title_short | On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$ |
| title_sort | on the regularity of the growth of the modulus and argument of an entire function in the metric of $l^p [0, 2π]$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4869 |
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