COMPOSITION OPERATOR ON FINITE TYPE MODEL DOMAINS AND CERTAIN WEIGHTED BERGMAN SPACES OVER THE UNIT BALL

Abstract

We give a characterization for the boundedness of a composition operator on the Bergman space over the two dimensional finite type model domains. For which, we study the boundedness of the composition operators on some singular weighted Bergman space over the two dimensional unit ball. We investigate composition operators on these singular weighted Bergman spaces over the unit ball with smooth symbols, and provide various interesting examples which reveal quite different phenomena from those on the usual weighted Bergman spaces over the unit ball.