Smoothness morrey spaces and differences : characterizations and applications

In his doctoral thesis the author studies the properties of Triebel-Lizorkin-Morrey spaces and Besov-Morrey spaces. For that purpose in a first step we prove characterizations in terms of higher order differences for those spaces. In connection with that we obtain sufficient and necessary conditions concerning the parameters. Moreover we also find characterizations in terms of differences for the diamond spaces associated to the Triebel-Lizorkin-Morrey spaces. In the second part of the thesis we use the characterization by differences to prove further properties of Triebel-Lizorkin-Morrey spaces. So on the one hand we study the behavior of some test functions. On the other hand we deal with complex interpolation of Triebel-Lizorkin-Morrey spaces on bounded Lipschitz domains. Finally we prove some results concerning the boundedness of truncation operators in the context of Triebel-Lizorkin-Morrey spaces.