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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On homogeneous polynomials on a complex ball


Authors: J. Ryll and P. Wojtaszczyk
Journal: Trans. Amer. Math. Soc. 276 (1983), 107-116
MSC: Primary 32A35; Secondary 32A05
MathSciNet review: 684495
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Abstract: We prove that there exist $ n$-homogeneous polynomials $ {p_n}$ on a complex $ d$-dimensional ball such that $ {\left\Vert {{p_n}} \right\Vert _\infty} = 1$ and $ {\left\Vert {{p_n}} \right\Vert _2} \geqslant \sqrt \pi {2^{- d}}$. This enables us to answer some questions about $ {H_p}$ and Bloch spaces on a complex ball. We also investigate interpolation by $ n$-homogeneous polynomials on a $ 2$-dimensional complex ball.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0684495-9
Article copyright: © Copyright 1983 American Mathematical Society