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Multipliers of Cauchy integrals of logarithmic potentials
Published online by Cambridge University Press: 26 February 2010
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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
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