On homogeneous polynomials on a complex ball

Ryll, J.; Wojtaszczyk, P.

doi:10.1090/S0002-9947-1983-0684495-9

On homogeneous polynomials on a complex ball
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by J. Ryll and P. Wojtaszczyk

Trans. Amer. Math. Soc. 276 (1983), 107-116

DOI: https://doi.org/10.1090/S0002-9947-1983-0684495-9

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Abstract:

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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