This note characterizes complex symmetric weighted composition-differentiation operators on Hardy space H², highlighting their relation with the conjugation operator.
In this note, we completely characterize the complex symmetric weighted composition-differentiation operator on the Hardy space H² with respect to the conjugation operator Cλ,ξ. The normal and self-adjoint of weighted composition-differentiation operators on the Hardy space H² are also studied. We also give the results on S²α,β and H²₁(D).
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Liu et al. (2025) studied this question.
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