Abstract
This paper characterizes the boundedness and compactness of the weighted differentiation composition operator from weighted Bergman space to n th weighted space on the unit disk of ≤.2000 Mathematics Subject Classification: Primary: 47B38; Secondary: 32A37, 32H02, 47G10, 47B33.
Highlights
Let D be the open unit disk in the complex space ≤, dA the Lebesegue measure on D normalized so that A(D) = 1
From (1), (6), and (7), we know that Dmφ,u : Apα → ωμ(n) is bounded
We show that for each s Î {m, m + 1,..., m + n}, there are constants c1, c2,..., cn+1, such that, gw(s)(w) =
Summary
We characterize the boundedness and compactness of the operator Dmφ,u from Apα to nth weighted space. For the case of Dmφ,u : Apα → ωμ(n), we have the following results: Theorem 1. (2b) Dmφ,u : Apα → ωμ(n,0)is compact if and only if Dmφ,u : Apα → ωμ(n,0)is bounded and for each k Î {0, 1,..., n}, μ(z) lim
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