Function theory in spaces of uniformly convergent Fourier series

Saccone, Scott

doi:10.1090/S0002-9939-99-05361-7

Function theory in spaces of uniformly convergent Fourier series
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Proc. Amer. Math. Soc. 128 (2000), 1813-1823 Request permission

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 $H^{\scriptscriptstyle \infty }$ to the space $H^{\scriptscriptstyle \infty }_{\scriptscriptstyle U}$ of bounded analytic functions whose partial Fourier sums are uniformly bounded.

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