Geodesic
Toeplitz operators on Bergman spaces and Hardy multipliers
Wolfgang Lusky 1   ; Jari Taskinen 2
1 FB 17, Mathematik und Informatik Universität Paderborn D-33098 Paderborn, Germany
2 Department of Mathematics and Statistics University of Helsinki P.O. Box 68 FI-00014 Helsinki, Finland
Studia Mathematica, Tome 204 (2011) no. 2, pp. 137-154 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study Toeplitz operators $T_a$ with radial symbols in weighted Bergman spaces $A_\mu ^p$, $1 p \infty $, on the disc. Using a decomposition of $A_\mu ^p$ into finite-dimensional subspaces the operator $T_a$ can be considered as a coefficient multiplier. This leads to new results on boundedness of $T_a$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of $T_a$ for $a$ satisfying an assumption on the positivity of certain indefinite integrals.
DOI : 10.4064/sm204-2-3
Keywords: study toeplitz operators radial symbols weighted bergman spaces infty disc using decomposition finite dimensional subspaces operator considered coefficient multiplier leads results boundedness shows connection hardy space multipliers using another method prove necessary sufficient condition boundedness satisfying assumption positivity certain indefinite integrals

Wolfgang Lusky  1   ; Jari Taskinen  2

1 FB 17, Mathematik und Informatik Universität Paderborn D-33098 Paderborn, Germany
2 Department of Mathematics and Statistics University of Helsinki P.O. Box 68 FI-00014 Helsinki, Finland 
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Wolfgang Lusky; Jari Taskinen. Toeplitz operators on Bergman spaces and Hardy multipliers. Studia Mathematica, Tome 204 (2011) no. 2, pp. 137-154. doi: 10.4064/sm204-2-3

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