The Properties Of Product Of Differentiation And Composition Operators On Some Function Spaces

In this paper, we mainly use the theory of function space to study the compactness and boundedness of product of differentiation and composition operators on the space of analytic function.We obtain a sufficient and a necessary condition for DCφ,（or CφDm） of product of differentiation and composition operator is compact on the Logarithmic-Bloch space, CφDmoperator is compact and bounded on the LogarithmicBloch type(Blogβα) space.At the same time,we also take into account the compactness and boundedness of ?CφDm2of 2-th weighted composition followed and proceeded by differentiation operator from Zygmund spaces to Bloch-type spaces,we obtain corresponding equivalent conditions.