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.

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