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 to the space HU of bounded analytic functions whose partial Fourier sums are uniformly bounded.

Original languageEnglish
Pages (from-to)1813-1823
Number of pages11
JournalProceedings of the American Mathematical Society
Volume128
Issue number6
StatePublished - Dec 1 2000

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