Here we introduce the th weighted space on the upper half-plane in the complex plane . For the case , we call it the Zygmund-type space, and denote it by . The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator from the Hardy space on the upper half-plane, to the Zygmund-type space, where is an analytic self-map of the upper half-plane.
"Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane." Abstr. Appl. Anal. 2009 1 - 8, 2009. https://doi.org/10.1155/2009/161528