Function theory in spaces of uniformly convergent Fourier series
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Abstract:
We study spaces of continuous functions on the unit circle with uniformly convergent Fourier series and show they possess such Banach space properties as the Pełczyński property, the Dunford-Pettis property and the weak sequential completeness of the dual space. We also prove extensions of theorems of Mooney and Sarason from the Hardy space $H^{\scriptscriptstyle \infty }$ to the space $H^{\scriptscriptstyle \infty }_{\scriptscriptstyle U}$ of bounded analytic functions whose partial Fourier sums are uniformly bounded.References
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Additional Information
- Scott F. Saccone
- Affiliation: Department of Mathematics, Campus Box 1146, Washington University, Saint Louis, Missouri 63130
- Address at time of publication: Department of Mathematics, 202 Mathematical Sciences Building, The University of Missouri, Columbia, Missouri 65211
- Email: saccone@math.missouri.edu
- Received by editor(s): August 4, 1998
- Published electronically: October 29, 1999
- Additional Notes: The author was partially supported by National Science Foundation grant DMS 9705851.
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1813-1823
- MSC (1991): Primary 46E15, 32C15
- DOI: https://doi.org/10.1090/S0002-9939-99-05361-7
- MathSciNet review: 1664367