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On bases in the disc algebra


Author: J. Bourgain
Journal: Trans. Amer. Math. Soc. 285 (1984), 133-139
MSC: Primary 46J15; Secondary 46B15, 46E15
DOI: https://doi.org/10.1090/S0002-9947-1984-0748834-3
MathSciNet review: 748834
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Abstract: It is shown that the disc algebra has no Besselian basis. In fact, concrete minorations on certain Lebesgue functions are obtained. A consequence is the nonisomorphism of the disc algebra and the space of uniformly convergent Fourier series on the circle.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0748834-3
Article copyright: © Copyright 1984 American Mathematical Society