COMPACT COMPOSITION OPERATORS ON WEIGHTED HILBERT SPACES.

Let φ be an analytic self-map of open unit disk 픽. A composition operator is defined as (C_φf)(z) = f(_φ(z)), for z ∈ 픽and f analytic on 픽. Given an admissible weight w, the weighted Hilbert space H_w consists of all analytic functions f such that ... = |f(0)|² + ∫_픽 |f'(z)\²w(z)dA(z) is finite. In this paper, we study composition operators acting between weighted Bergman space A_α^² and the weighted Hilbert space H_w. Using generalized Nevalinna counting functions associated with w, we characterize the bounded-ness and compactness of these composition operators. [ABSTRACT FROM AUTHOR]