The convergence classes for analytic functions in the Reinhardt domains - Salo, T.M.; Tarnovecka, O.Yu. (Carpathian Mathematical Publications, 2018)
Let L^0 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(e^x)L^0 and function βL^0 such that _1^+∞α(x)β(x)dx<+∞. In the article it is proved the following theorem: if f(z)=_\|n\|=0^+∞a_nz_n, zC^p, is analytic function in the bounded Reinhard domain GC^p, then the condition _R_0^1 α(^+ M_G(R,f)) (1-R)^2β(1/(1-R))d R<+∞, M_G(R,f)={|F(Rz)|zG}, yields that _k=0^+∞(α(k)-α(k-1)) β_1(k/^+|A_k|)<+∞, β_1(x)= _x^+∞ dtβ(t),A_k={|a_n|\|n\|=k}.