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Function theory in spaces of uniformly convergent Fourier series
Author(s):
Scott
F.
Saccone
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1813-1823.
MSC (1991):
Primary 46E15, 32C15
Posted:
October 29, 1999
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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  to the space  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
DOI:
10.1090/S0002-9939-99-05361-7
PII:
S 0002-9939(99)05361-7
Received by editor(s):
August 4, 1998
Posted:
October 29, 1999
Additional Notes:
The author was partially supported by National Science Foundation grant DMS 9705851.
Communicated by:
Dale Alspach
Copyright of article:
Copyright
2000,
American Mathematical Society
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