Sharp multiplier estimates are established for the higher-order Schwarzian derivatives of the Koebe function, extending Shimorin's result via an explicit formula and a prior theorem.
On the norms of the multiplication operators between weighted Bergman spaces
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In this paper, we study the norms of multiplication operators acting between weighted Bergman spaces. First, we provide a proof for a norm estimate previously announced in our recent paper \cite{Jin-c}. Second, we establish a sharp norm estimate for certain special multiplication operators between weighted Bergman spaces, a result that is novel to the literature. Finally, we also discuss the connections between the Brennan conjecture and related multiplier norms induced by the Schwarzian derivative of univalent functions.
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Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function
Sharp multiplier estimates are established for the higher-order Schwarzian derivatives of the Koebe function, extending Shimorin's result via an explicit formula and a prior theorem.