Toeplitz operators on Bergman spaces and Hardy multipliers

• Autorzy: Wolfgang Lusky , Jari Taskinen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 2
• Strony: 137-154

Daty

wydano

2011

Twórcy

autor

Wolfgang Lusky

• FB 17, Mathematik und Informatik, Universität Paderborn, D-33098 Paderborn, Germany

autor

Jari Taskinen

• Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsinki, Finland

Identyfikatory

DOI

10.4064/sm204-2-3