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arXiv · 1805.06838

Sums of Weighted Differentiation Composition Operators

Soumyadip Acharyya·Timothy Ferguson
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Abstract

We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions of unit norm. The solution obtained has norm bounded by a constant independent of the points chosen. As a direct application, we obtain a characterization of the order-boundedness of a sum of products of weighted composition and differentiation operators acting between weighted Bergman spaces. We also characterize the compactness of such operators that map a weighted Bergman space into the space of bounded analytic functions.

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Soumyadip Acharyya, Timothy Ferguson. 2018-05-17. Sums of Weighted Differentiation Composition Operators. https://arxiv.org/abs/1805.06838

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