Multipliers of Bergman spaces into Lebesgue spaces

Abstract

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 thatprovided 0<p≦q.