Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some characterizations of $C(\mathcal M)$


Author: Christopher J. Bishop
Journal: Proc. Amer. Math. Soc. 124 (1996), 2695-2701
MSC (1991): Primary 46J10
MathSciNet review: 1326997
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that a function $f$ on the unit disk extends continuously to $\mathcal M$, the maximal ideal space of $H^\infty (\mathbb D)$ iff it is uniformly continuous (in the hyperbolic metric) and close to constant on the complementary components of some Carleson contour.


References [Enhancements On Off] (What's this?)

  • 1. Sheldon Axler and Allen Shields, Extensions of harmonic and analytic functions, Pacific J. Math. 145 (1990), no. 1, 1–15. MR 1066396
  • 2. C.J. Bishop A distance formula for algebras on the disk, Pacific J. Math. (to appear).
  • 3. John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
  • 4. Kenneth Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74–111. MR 0215102
  • 5. O. V. Ivanov, Nontangential limits and the Shilov boundary of the algebra 𝐻^{∞}, Dokl. Akad. Nauk Ukrain. SSR 7 (1991), 5–8, 177 (Russian, with English summary). MR 1157940

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46J10

Retrieve articles in all journals with MSC (1991): 46J10


Additional Information

Christopher J. Bishop
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Email: bishop@math.sunysb.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03328-X
Keywords: Harmonic functions, holomorphic functions, function algebras, maximal ideal space, Carleson measures, uniform approximation
Received by editor(s): November 23, 1994
Received by editor(s) in revised form: February 24, 1995
Additional Notes: The author is partially supported by NSF Grant DMS 92-04092 and an Alfred P. Sloan research fellowship.
Communicated by: T. W. Gamelin
Article copyright: © Copyright 1996 American Mathematical Society