Integral Equations and Operator Theory

, Volume 45, Issue 3, pp 309–318

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

  • Rick Chartrand
Research article

DOI: 10.1007/s000200300007

Cite this article as:
Chartrand, R. Integr. equ. oper. theory (2003) 45: 309. doi:10.1007/s000200300007


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.

Keywords. Multipliers, Carleson measures, Dirichlet-type spaces.¶Mathematics Subject Classification (2000). Primary 46E20.

Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  • Rick Chartrand
    • 1
  1. 1.Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S.Morgan St. (MC 249), Chicago, IL 60607, USA. E-mail: rchartra@math.uic.eduUS