This analysis characterizes boundedness and compactness of differentiation operators in weighted Bergman spaces, suggesting implications for functional analysis.
Let be the upper half‐plane in the complex plane , and be the weighted Bergman space defined on . We characterize the boundedness, compactness, and order boundedness of the weighted differentiation composition operators between weighted Bergman spaces. We also characterize the order boundedness of the finite sums of weighted differentiation composition operators between these spaces.
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Jiang et al. (2026) studied this question.