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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On homogeneous polynomials on a complex ball
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by J. Ryll and P. Wojtaszczyk PDF
Trans. Amer. Math. Soc. 276 (1983), 107-116 Request permission


We prove that there exist $n$-homogeneous polynomials ${p_n}$ on a complex $d$-dimensional ball such that ${\left \| {{p_n}} \right \|_\infty } = 1$ and ${\left \| {{p_n}} \right \|_2} \geqslant \sqrt \pi {2^{- d}}$. 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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 107-116
  • MSC: Primary 32A35; Secondary 32A05
  • DOI:
  • MathSciNet review: 684495