The dissertation by MSc Bin Liu is related with classical function spaces (such as weighted Bergman spaces and Hardy spaces) and operators acting on them.
The dissertation by MSc Bin Liu is related with classical function spaces (such as weighted Bergman spaces and Hardy spaces) and operators acting on them. The dissertation contains several new results that improve several old ones, which aim at a more comprehensive understanding of operator theory and function spaces. In this dissertation, the closure of the weighted Bergman and Dirichlet spaces in the Bloch norm is described in terms of a kind of Lusin area function and natural level sets. On the other hand, composition operators and certain closely related operators on the weighted Bergman spaces were studied. The general tools and methods used to study composition operators lie under several theories, such as Khinchine’s inequality and Carleson measures.
For difference composition operators, Moorhouse solved the compactness problem for the difference operators on Aα2 . This line of research was continued by Saukko. He generalized Moorhouse’s result to the setting of Aαp . In dissertation, some of Saukko’s results were extended to the weighted Bergman spaces Aωp induced by doubling weights.
The doctoral dissertation of Master of Science Bin Liu, entitled Studies on classical function spaces and operators acting on them, will be examined at the Faculty of Science and Forestry on the 13th of August at 2 pm online. The opponent will be Professor Lino Feliciano Reséndis Ocampo, Universidad Autónoma Metropolitana, México, and the custos will be Professor Jouni Rättyä, University of Eastern Finland. The public examination will be held in English.
