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On the regularity of the growth of the modulus and argument of an entire function in the metric of Lp [0, 2π]

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Abstract

Under sufficiently general assumptions, we describe sets of entire functions f, sets of growing functions λ, and sets of complex-valued functions H from Lp [0, 2π], p ∈ [1, + ∞], for which

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

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Authors and Affiliations

  1. Lvov University, Lvov

    R. Z. Kalynets’ & A. A. Kondratyuk

Authors
  1. R. Z. Kalynets’
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  2. A. A. Kondratyuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 889–896, July, 1998.

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Kalynets’, R.Z., Kondratyuk, A.A. On the regularity of the growth of the modulus and argument of an entire function in the metric of Lp [0, 2π]. Ukr Math J 50, 1009–1018 (1998). https://doi.org/10.1007/BF02528830

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  • DOI: https://doi.org/10.1007/BF02528830

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