Journal of Operator Theory

Volume 48, Issue 1, Summer 2002 pp. 2-13.

Toeplitz operators on Dirichlet-Type spaces

Authors: Rick Chartrand
Author institution: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan St. (MC 249), Chicago, IL 60607, USA

Summary: In this paper, variants of the classical Toeplitz operators on $H^2$ are studied. A characterization is obtained for the bounded, harmonic symbols giving rise to a bounded Toeplitz operator on a Dirichlet-type space. The relationship between the characterizing condition and multipliers of the holomorphic and harmonic Dirichlet spaces is examined.

Keywords: Toeplitz operator, Dirichlet space, Dirichlet-type spaces

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