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On radial variation of holomorphic functions with lp Taylor coefficients

Published online by Cambridge University Press:  20 January 2009

D. J. Hallenbeck  and
K. Samotij
D. J. Hallenbeck
Affiliation:
Department of Mathematical SciencesUniversity of DelawareNewark, Delaware 19716
K. Samotij
Affiliation:
Instytut MatematykiPolitechniki WroclawskiejWybrzeŻc St. Wyspiańskiego 27Wroclaw, Poland
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Abstract

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Suppose is holomorphic in Δ = {z:|z|<l} and (an)∈lp where 1≦p≦2. We prove that for k=1,2,…, and almost every θ. This result is sharp in the following sense: Let p∈[1,2] and ε(r) be a positive function defined on [0,1] such that limr→1-ε(r)=0. Then there exists a function holomorphic in Δ with (an)∈lp such that

for each k>1/p.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 3 , October 1990 , pp. 475 - 481
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

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