On The Space Of Analytic Functions Of ¦Á-complex Operator

In this paper we investigateα-composition operator C_?^αbetween some spaces of analytic function on the unit D of the complex plane. The spaces we considered here contain the Bloch-type spaces B^α, which consist of all analytic functions f on D such that.and the spaces F(p,q,s), 0 ?^αdefined byinduced by analytic function (?): D→D defines an operator on analytic function spaces. We characterize, in function theoretic terms, in what conditions the operator C_?^αfrom Bloch-type spaces to Bloch-type spaces; from Bloch-type spaces to F(p,q,s)and F(p,q,s)to Bloch-type spaces is bounded repectively compact.