October 15, 2025

Complex symmetric weighted composition-differentiation operators on Hardy-type spaces

Key Points

The study characterizes complex symmetric weighted composition-differentiation operators on Hardy space H².
Results on normal and self-adjoint operators are thoroughly explored, demonstrating regularity in this class of operators.
Key results concerning S²_α,β and the Hardy space H²_1(ℝ) provide deeper insights into the structure of these operators.
Connections between conjugation operators and weighted composition-differentiation operators enhance our understanding of operator theory.

Abstract

In this note, we completely characterize the complex symmetric weighted composition-differentiation operator on the Hardy space H² with respect to the conjugation operator C,. The normal and self-adjoint of weighted composition-differentiation operators on the Hardy space H² are also studied. We also give the results on S², and H²₁ (D).

Complex symmetric weighted composition-differentiation operators on Hardy-type spaces

Key Points

Abstract

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