Localization and Toeplitz operators with complex Borel measure symbols on weighted Bergman spaces
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Date
2021-05-28
Authors
Sadeghi, Mohammad
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Abstract
We extend the definition of weak localization to the weighted Bergman spaces of the unit ball, L^2_a(B_n, dV_alpha), for alpha>-1. We prove that a Toeplitz operator with a complex Borel measure symbol whose total variation is Carleson is weakly localized on L^2_a(B_n, dV_alpha). We extend the definitions of strongly localized and sufficiently localized operators defined in the paper of the Ph.D. candidate and Prof. N. Zorboska, to the weighted Bergman spaces L^2_a(B_n, dV_alpha) and show that they are also weakly localized. We also show that bounded Toeplitz operators with BMO^1 symbols are strongly (and therefore also weakly) localized. Finally, we prove that the Toeplitz operators induced by the complex Borel measures with Carleson total variation are weakly localized on the spaces L^2_a(omega) with the weight omega in class E.
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Localization, Toeplitz Operators, Complex Measures, Carleson Measures, Weighted Bergman Spaces
Citation
Localization, Carleson measure, and BMO Toeplitz operators on the Bergman space, with Nina Zorboska, J. Math. Anal. Appl. 485 (2020),123829