Abstract
We describe the evolution of boundary interpolation sets between the disk-algebra and Holder spaces of analytic functions. For the disk-algebra, interpolation sets are sets of zero measure, while for Holder spaces of order α, interpretation sets are porous. For the Holder-type classes corresponding to a continuity modulus ω, a necessary condition for free interpolation turns into a certain condition of ω-porosity. Any set of zero measure is ω-porous for some ω. We establish a Muckenhoupt-type estimate; such estimates may be useful in the proof of sufficiency of ω-porosity conditions. Bibliography: 7 titles.
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