The convergence classes for analytic functions in the Reinhardt domains
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 2
Abstract
Let L0 be the class of positive increasing on [1,+∞) functions l such that l((1+o(1))x)=(1+o(1))l(x) (x→+∞). We assume that α is a concave function such that α(ex)∈L0 and function β∈L0 such that ∫+∞1α(x)/β(x)dx<+∞. In the article it is proved the following theorem: if f(z)=+∞∑∥n∥=0anzn, z∈Cp, is analytic function in the bounded Reinhard domain G⊂Cp, then the condition 1∫R0α(ln+MG(R,f))(1−R)2β(1/(1−R))dR<+∞, MG(R,f)=sup{|F(Rz)|:z∈G},yields that +∞∑k=0(α(k)−α(k−1))β1(k/ln+|Ak|)<+∞,β1(x)=+∞∫xdtβ(t),Ak=max{|an|:∥n∥=k}.
Authors and Affiliations
T. M. Salo, O. Yu. Tarnovecka
Keywords
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- EP ID EP535588
- DOI 10.15330/cmp.10.2.408-411
- Views 49
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