Abstract
Recently the author proved that the Hummel–Scheinberg–Zalcman conjecture of 1977 on coefficients of nonvanishing Hp functions is true for all p = 2m, m ϵ ℕ, i.e., for the Hilbertian Hardy spaces H2m. As a consequence, this also implies the proof of the Krzyz conjecture for bounded nonvanishing functions, which originated this direction.
In the present paper, we solve the problem for all spaces Hp with p ≥ 2.
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In memory of Reiner Kühnau
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 19, No. 4, pp. 517–540, October–December, 2022.
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Krushkal, S.L. Two coefficient conjectures for nonvanishing Hardy functions, II. J Math Sci 270, 449–466 (2023). https://doi.org/10.1007/s10958-023-06357-6
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DOI: https://doi.org/10.1007/s10958-023-06357-6