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arXiv · 2604.20326

Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function

Jianjun Jin
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Abstract

In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function. This extends a related result by Shimorin. The proof of our new theorem relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work. We finally point out that the Koebe function is still the extremal function for certain higher-order Schwarzians of the univalent functions.

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Jianjun Jin. 2026-04-22. Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function. https://arxiv.org/abs/2604.20326

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