Multipliers of Bergman spaces into Lebesgue spaces

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 .