2019
Том 71
№ 8

All Issues

Kalinets R. Z.

Articles: 1
Article (Ukrainian)

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

Kalinets R. Z., Koval’chuk Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 889-896

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 $$\left\{ {\frac{1}{{2\pi }}\int\limits_0^{2\pi } {|\log f(re^{i\theta } ) - \lambda (r)H(\theta )|^p } d\theta } \right\}^{1/p} = o(\lambda (r)),r \to \infty.$$