Boundary interpolation sets for holomorphic functions smooth to the boundary and BMO
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- by Joaquim Bruna
- Trans. Amer. Math. Soc. 264 (1981), 393-409
- DOI: https://doi.org/10.1090/S0002-9947-1981-0603770-5
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Abstract:
Let ${A^p}$ denote 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 ${A^p}$, that is, those closed sets $E \subset T$ such that every function in ${C^p}(E)$ extends to a function in ${A^p}$. We also give a constructive proof of the corresponding result for ${A^\infty }$ (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 $E$.References
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Bibliographic Information
- © Copyright 1981 American Mathematical Society
- 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