Norm and Compactness of a Polynomial Differentiation Composition Operator on the Unit Disc

Key Points

• This research investigates the properties of polynomial differentiation composition operators in the context of Cauchy transforms and weighted Bergman spaces.
• Characterization of boundedness in terms of operator symbols and parameters.
• Calculation of the operator norm based on defined quantities.
• Identification of necessary and sufficient conditions for operator compactness.
• Boundedness of the operator is framed using specific operator symbols and parameters.
• The norm of the polynomial differentiation operator is explicitly calculated.
• Compactness conditions are thoroughly detailed, providing a structured framework.