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Sums of Weighted Differentiation Composition Operators
We solve an interpolation problem in involving specifying a set
of (possibly not distinct) points, where the derivative
at the 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.Comment: 13 page