Wiman's inequality for analytic functions in D×C with rapidly oscillating coefficients
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 1
Abstract
Let A2 be a class of analytic function f represented by power series of the from f(z)=f(z1,z2)=+∞∑n+m=0anmzn1zm2 with the domain of convergence T={z∈C2:|z1|<1,|z2|<+∞} such that ∂∂z2f(z1,z2)≢0 in T and there exists r0=(r01,r02)∈[0,1)×[0,+∞) such that for all r∈(r01,1)×(r02,+∞) we have r1∂∂r1lnMf(r)+lnr1>1, where Mf(r)=∑+∞n+m=0|anm|rn1rm2. Let K(f,θ)={f(z,t)=∑+∞n+m=0anme2πit(θn+θm):t∈R} be class of analytic functions, where (θnm) is a sequence of positive integer such that its arrangement (θ∗k) by increasing satisfies the condition θ∗k+1/θ∗k≥q>1,k>0. For analytic functions from the class K(f,θ) Wiman's inequality is improved.
Authors and Affiliations
A. Kuryliak, V. L. Tsvigun
Keywords
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- DOI 10.15330/cmp.10.1.133-142
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