The Composition Operators Between Logarithmic Weighted Bloch Spaces

This dissertation discusses the bounded-ness and compactness conditions of weighted composition operators from the logarithmic weighted Bloch space to Bloch-type spaces.It consists of three chapters.In the first chapter,we will carry on a comprehensive summary about the research background as well as the conclusions that, we, will given.In the second chapter, the briefly sufficient and necessary conditions are given for which the weighted composition operator is compact operator from the logarithmic weighted Bloch space to Bloch type spaces (a> 1) in the disc, that is the theorem 2.3.2. At the same time, we also gives a practical theorem, that is the theorem 2.3.1.In the third chapter, we will extend the necessary and sufficient conditions of weighted composition operator is a bounded operator or a compact operator from the logarithmic weighted Bloch space to Bloch type spaces (a> 1) from the disc to the unit ball. At the same time, we also simplifies the result of a complex variable circumstances, that is the theorem 3.3.1 and theorem 3.3.2. In addition we also gives a useful lemma, that is the lemma 3.2.1.