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.
|Number of pages||11|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Dec 1 2000|