Operators On The Analytic Function Spaces

In this thesis we study characterization of operators in the Hp spaces, Ba spaces , BMOA spaces, Hlog∞spaces,Hμ∞spaces in the unit disk. We give the Lipschitz type characterization of logarithmic Bloch space. This paper is divided into five sections:In Charpter 1, we mainly introduce some definitions and give some results about operators theory.In Charpter 2, we mainly concerned with the boundedness and compactness of the weighted composition operators from Hp spaces to Ba spaces. As application, we attain the multipliers M(Hp,Bα) and compact multipliers Mo(Hp,Bα).In Charpter 3, we mainly concerned with the boundedness and compactness of the operators DC from Hp spaces to Hμ∞(HμO∞) spaces. We also estimate the essential norm ||DCψ||e,Hp→Hμ∞.In Charpter 4, we mainly concerned with the boundedness and compactness of the Volterra operators from Hlog∞to B (BMOA) spaces.In Charpter 5, we define d^ and illustrate it is a distance on Blogβα.Then we give the Lipschitz type characterization of logarithmic Bloch-type space.