Multipliers and Carleson Measures for $D(\mu)$

Abstract.

In this paper, the multipliers of the Dirichlet-type space $D(\mu)$ associated with a positive measure $\mu$ on the unit circle are characterized in terms of $\mu$-Carleson measures. A geometric description of $\mu$-Carleson measures is given for the cases of $\mu$ being absolutely continuous with an $A_{2}$ weight, and of $\mu$ being a finite sum of atoms.