Carleson Measures, Riemann–Stieltjes and Multiplication Operators on a General Family of Function Spaces

摘要

Let μ be a nonnegative Borel measure on the unit disk of the complex plane. We characterize those measures μ such that the general family of spaces of analytic functions, F(p, q, s), which contain many classical function spaces, including the Bloch space, BMOA and the Q_s spaces, are embedded boundedly or compactly into the tent-type spaces T_(p,s)~∞(μ). The results are applied to characterize boundedness and compactness of Riemann–Stieltjes operators and multiplication operators on F(p, q, s).