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Journal of Operator Theory

Volume 68, Issue 1, Summer 2012  pp. 131-140.

Weighted BMO and Toeplitz operators on the Bergman space $A^1$

Authors:  J. Taskinen (1) and J.A. Virtanen (2)
Author institution: (1) Department of Mathematics and Statistics, University of Helsinki, Helsinki, 00014, Finland
(2) Courant Institute of Mathematical Sciences, New York University, New York, 10012, U.S.A.

Summary:  We generalize our recent results on the boundedness and compactness of Toeplitz operators to the Bergman space $A^1$ on the unit disc. While the natural condition for the symbols leads to $BMO_\partial$-type symbol classes, the inevitable logarithmic correction for the nonreflexive case requires a separate treatment of $BA$-and $BO$-type symbols.

Keywords:  Toeplitz operator, boundedness, compactness, bounded mean oscillation, Bergman space $A^1$

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