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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 1465–1479 | Cite as

Sums of Weighted Differentiation Composition Operators

  • Soumyadip Acharyya
  • Timothy FergusonEmail author
Article
  • 76 Downloads

Abstract

We solve an interpolation problem in \(A^p_\alpha \) involving specifying a set of (possibly not distinct) n points, where the \(k{\text {th}}\) derivative at the \(k{\text {th}}\) 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.

Keywords

Weighted composition operator Iterated differentiation operator Order-bounded Compactness Bergman space Hardy space 

Notes

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Authors and Affiliations

  1. 1.Department of Math, Physical and Life SciencesEmbry-Riddle Aeronautical University WorldwideDaytona BeachUSA
  2. 2.Department of MathematicsUniversity of AlabamaTuscaloosaUSA

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