LAUSR

Let D be the open unit disk in the complex plane C and let H(D) denote the space of all analytic functions on D. For p > 0 and α > −1 we consider the Bergman spaces Aα = L (D, dAα) ∩H(D), where dAα(z) = (α + 1)(1− |z| ) dA(z). Here dA is area measure on C normalized so that A(D) = 1. It is well known that a function f ∈ H(D) belongs to Aα if and only if the function (1− |z|)f (z) belongs to L(D, dAα). Moreover, we have