Applications of the spaces of homogeneous polynomials to some problems on the ball algebra
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- by J. Bourgain PDF
- Proc. Amer. Math. Soc. 93 (1985), 277-283 Request permission
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.References
- J. Bourgain, Bilinear forms on $H^{\infty }$ and bounded bianalytic functions, Trans. Amer. Math. Soc. 286 (1984), no. 1, 313–337. MR 756042, DOI 10.1090/S0002-9947-1984-0756042-5
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- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 277-283
- MSC: Primary 46E15; Secondary 32A35, 46J15, 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770536-4
- MathSciNet review: 770536