Key points are not available for this paper at this time.
Let U be the open unit disk in the complex plane endowed with normalized Lebesgue measure m . will denote the usual Lebesgue space with respect to m , with 0< p <+∞. The Bergman space consisting of the analytic functions in will be denoted . Let μ be some positivefinite Borel measure on U . It has been known for some time (see 6 and 9) what conditions on μ are equivalent to the estimate: There is a constant C such that provided 0< p ≦ q .
Daniel H. Luecking (Sat,) studied this question.