Boundary interpolation sets for holomorphic functions smooth to the boundary and bmo

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Abstract

Let Apdenote the class of holomorphic functions on the unit disc whose first p-derivatives belong to the disc algebra. We characterize the boundary interpolation sets for Apthat is, those closed sets E Ì T such that every function inCP(E) extends to a function in ApWe also give a constructive proof of the corresponding result for A¥(see [1]). We show that the structure of these sets is in some sense related to BMO and that this fact can be used to obtain precise estimates of outer functions vanishingon E. © 1981 American Mathematical Society.
Original languageEnglish
Pages (from-to)393-409
JournalTransactions of the American Mathematical Society
Volume264
Issue number2
DOIs
Publication statusPublished - 1 Jan 1981

Keywords

  • BMO
  • BMOA
  • Boundary interpolation sets
  • Carleson sets
  • Lipschitz conditions
  • Outer functions

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