COMPOSITION OPERATORS ON GENERALIZED WEIGHTED NEVALINNA CLASS

Let phi be an analytic self-map of open unit disk D. The operator given by (C(phi)f)(z) = f((phi(z)), for z is an element of D and f analytic on D is called a composition operator. Let w be a weight function such that w is an element of L-1 (D, dA). The space we consider is a generalized weighted Nevanlinna class N-omega which consists of all analytic functions f on D such that parallel to f parallel to(omega) = integral(log+)(D)(vertical bar f(z))w(z)dA(z) is finite; that is, N-w is the space of all analytic functions belong to L-log+(D, wdA). In this paper we investigate, in terms of function-theoretic, composition operators on the space N-w. We give sufficient conditions for the boundedness and compactness of these composition operators.