A remark on Bourgain algebras on the disk
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- by Pratibha G. Ghatage, Shun Hua Sun and De Chao Zheng PDF
- Proc. Amer. Math. Soc. 114 (1992), 395-398 Request permission
Abstract:
It is shown that the Bourgain algebra ${X_b}$ of the space $X = {H^\infty }$ considered as a subalgebra of $\mathcal {U} = \operatorname {alg} \{ {H^\infty },{\overline H ^\infty }\}$ is ${H^\infty }(\mathbb {D}) + UC(\mathbb {D})$ where $UC(\mathbb {D})$ is the algebra of uniformly continuous functions on the open unit disk $\mathbb {D}$. This uses and extends a recent result of Cima-Janson-Yale on the Bourgain algebra of ${H^\infty }$ on $\partial \mathbb {D}$. Further, ${({X_b})_b} = {X_b}$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 395-398
- MSC: Primary 46J10; Secondary 30D55, 30H05, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1992-1065947-X
- MathSciNet review: 1065947