Complex symmetric weighted composition-differentiation operators on weighted Hardy spaces

Abstract

Complex symmetric weighted composition-differentiation operators on the weighted Hardy spaces $H^2\left(\beta \right)$ with respect to the standard conjugation are investigated. Our results partially answer a question from a paper of Lim and Khoi (2018) [12] and subsume several existing ones in the literature. We also study the classes of self-adjoint, normal, co-isometric and unitary weighted composition-differentiation operators on $H^2\left(\beta \right)$ as well as their relations with the property of complex symmetry.