Carleson Measure and Multipliers on Bergman Space

1. Introduction.In 1962, Carleson 2] proved the well known Carleson measure theorem for Hardy space. In 1975. Hastings 5] obtained an analogous theorem for Bergman space. In this paper we prove a Carleson type theorem for the quasi-normal weighted Bergman space using a way other than Hastings'.As an application we obtain a theorem on multiplier theory. This generalizes