Two Operators On Analytic Function Spaces And Cyclic Vectors In Q_p Space

In this paper, we mainly discuss the boundedness and compactness of the weighted composition operator from Hardy spaces H9(1≤q≤∞) to logarith-mic Hardy-Block type spaces BHp,L. We also give the boundedness of integral operators from analytic Morrey spaces to Block space. At the same time, we give a necessary and sufficient condition about the univalent function in the Qp space and the Qp,o space with0<p<1is cyclic. There are four chapters in the paper.In Chapte1, we mainly introduce some definitions of analytic function spaces, operators and cyclic. We also list some results to the thesis.In Chapter2, we concentrate in, the logarithmic Hardy-Block type spaces in the unit disk. A sufficient and necessary condition is given for weighted composition operators to be bounded or compact from Hardy spaces to logarithmic Hardy-Bloch type spaces. Also, a sufficient and necessary condition are obtained for which the pointwise multiplication operator is bounded on the logarithmic Hardy-Block type spaces.Chapter3is aimed at characterizations of the boundedness of integral operators from analytic Morrey spaces to Bloch space.In Chapter4, we are devoted to investigate the necessary and sufficient condi-tion about the univalent function in the Qp space with0<p<1is cyclic.