On Bases in the Disc Algebra

J. Bourgain
1984 Transactions of the American Mathematical Society  
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. Introduction. The purpose of this paper is to prove the following result on the disc algebra A. THEOREM. Assume m is a positive integer and (fk)i<k<n, {%k)i<k<n are biorthogonal sequences in A, A* resp., satisfying the properties:
doi:10.2307/1999476 fatcat:laewvjfzgvhdvdmtzey5bfniwq