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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Applications of the spaces of homogeneous polynomials to some problems on the ball algebra


Author: J. Bourgain
Journal: Proc. Amer. Math. Soc. 93 (1985), 277-283
MSC: Primary 46E15; Secondary 32A35, 46J15, 47B38
MathSciNet review: 770536
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Abstract: Denote by $ {B_2}$ the unit ball in $ {{\mathbf{C}}^2}$. The existence is shown of a uniformly bounded orthonormal basis in $ {H^2}({B_2})$, by constructing such systems in the spaces of homogeneous polynomials. In the second part of the paper, those spaces of homogeneous polynomials are exploited to disprove the existence of generalized analytic projections, the so-called $ ({i_p} - {\pi _p})$ property, for the ball algebra.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770536-4
PII: S 0002-9939(1985)0770536-4
Article copyright: © Copyright 1985 American Mathematical Society