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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Function theory in spaces
of uniformly convergent Fourier series


Author: Scott F. Saccone
Journal: Proc. Amer. Math. Soc. 128 (2000), 1813-1823
MSC (1991): Primary 46E15, 32C15
Published electronically: October 29, 1999
MathSciNet review: 1664367
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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 Pelczynski 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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05361-7
PII: S 0002-9939(99)05361-7
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
Article copyright: © Copyright 2000 American Mathematical Society