Toeplitz operators on Bergman spaces and Hardy multipliers

Wolfgang Lusky; Jari Taskinen

Studia Mathematica, Tome 204 (2011), p. 137-154 / Harvested from The Polish Digital Mathematics Library

Résumé

We study Toeplitz operators $T_{a}$ with radial symbols in weighted Bergman spaces $A_{μ}^{p}$ , 1 < p < ∞, on the disc. Using a decomposition of $A_{μ}^{p}$ 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.

Publié le : 2011-01-01

Zbl 1237.47034

EUDML-ID : urn:eudml:doc:285518

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     title = {Toeplitz operators on Bergman spaces and Hardy multipliers},
     journal = {Studia Mathematica},
     volume = {204},
     year = {2011},
     pages = {137-154},
     zbl = {1237.47034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-2-3}
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Wolfgang Lusky; Jari Taskinen. Toeplitz operators on Bergman spaces and Hardy multipliers. Studia Mathematica, Tome 204 (2011) pp. 137-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-2-3/