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

Author:
Joaquim Bruna

Journal:
Trans. Amer. Math. Soc. **264** (1981), 393-409

MSC:
Primary 30E05; Secondary 30D60, 42A50

DOI:
https://doi.org/10.1090/S0002-9947-1981-0603770-5

MathSciNet review:
603770

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the class of holomorphic functions on the unit disc whose first -derivatives belong to the disc algebra. We characterize the *boundary interpolation sets* for , that is, those closed sets such that every function in extends to a function in .

We also give a constructive proof of the corresponding result for (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 vanishing on .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0603770-5

Keywords:
Boundary interpolation sets,
Carleson sets,
Lipschitz conditions,
BMO,
BMOA,
outer functions

Article copyright:
© Copyright 1981
American Mathematical Society