On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$

• Date: 1998
• Main Authors: Kalinets, R. Z., Koval’chuk, Yu. A., Калинець, Р. З., Ковальчук, Ю. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4869
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 )|^...