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Toeplitz operators on Bergman spaces of polygonal domains

Part of: Special classes of linear operators

Published online by Cambridge University Press:  26 June 2019

Paula Mannersalo
Paula Mannersalo*
Affiliation:
Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki, Finland (paula.mannersalo@gmail.com)
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Abstract

We study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces Ap(Ω), 1 < p < ∞, where Ω ⊂ ℂ is a bounded simply connected domain with polygonal boundary. We give sufficient conditions for the boundedness of generalized Toeplitz operators in terms of ‘averages’ of symbol over certain Cartesian squares. We use the Whitney decomposition of Ω in the proof. We also give examples of bounded Toeplitz operators on Ap(Ω) in the case where polygon Ω has such a large corner that the Bergman projection is unbounded.

Keywords

Toeplitz operatorBergman spaceboundednesspolygonal domainlocally integrable symbolWhitney decompositionSchwarz–Christoffel formula

MSC classification

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 4 , November 2019 , pp. 1115 - 1136
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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