Essential Norms of Weighted Composition Operators from Hilbert Function Spaces into Zygmund-Type Spaces

Abstract

In this work, we provide an approximation of the essential norm of the weighted composition operators acting on a Hilbert function space and mapping into a Zygmund-type space, and give characterizations of the boundedness and compactness of such operators. Our results apply to a large class of weighted Hardy spaces, including the Hardy space H 2, the weighted Bergman space $${A^2_\alpha \,\, (\alpha \geq 1)}$$ , and the logarithmic Bergman space $${A^2_{\rm log}}$$ .