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Multipliers of Cauchy integrals of logarithmic potentials

Part of: Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  26 February 2010

D. J. Hallenbeck  and
K. Samotij
D. J. Hallenbeck
Affiliation:
Department Mathematical Sciences, University of Delaware, Newark, DE 19716, U.S.A.
K. Samotij
Affiliation:
Instytut Matematyki, Politechnika Wrocławska, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
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Extract

Let Δ = {z:|Z|<1}, Γ={z:|z|=1}, and ℳ denote the set of complex-valued Borel measures on Γ. Let Kα(z)=(1−z)−α for α>0 and K0(z)=log 1/(1−z). For α > 0 let ℱα denote the family of functions f on Δ having the property that there exists a measure μ∈ℳ such that

for |z|<1. When α=0, this condition is replaced by

MSC classification

Secondary: 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 397 - 405
Copyright
Copyright © University College London 1995

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References

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