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arXiv · 2211.16295

Quasiconformal deformations of nonvanishing $H^p$ functions and the Hummel-Scheinberg-Zalcman conjecture

Samuel L. Krushkal
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Abstract

Recently the author proved that the 1977 Hummel-Scheinberg-Zalcman conjecture on coefficients of nonvanishing $H^p$ functions is true for all $p = 2m, m \in \mathbb{N}$, i.e., for the Hilbertian Hardy spaces $H^{2m}$. As a consequence, this also implies a proof of the Krzyz conjecture for bounded nonvanishing functions which originated this direction. In the present paper, we solve the problem for all spaces $H^p$ with $p \ge 2$.

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Samuel L. Krushkal. 2022-11-29. Quasiconformal deformations of nonvanishing $H^p$ functions and the Hummel-Scheinberg-Zalcman conjecture. https://arxiv.org/abs/2211.16295

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