Function theory in spaces of uniformly convergent fourier series

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 H_U^∞ of bounded analytic functions whose partial Fourier sums are uniformly bounded.