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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… Click to show full abstract
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:
operators bergman;
bergman spaces;
toeplitz operators;
spaces polygonal;
polygonal domains
Journal Title: Proceedings of the Edinburgh Mathematical Society
Year Published: 2019
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Journal Title: Proceedings of the Edinburgh Mathematical Society
Year Published: 2019
Link to full text (if available)
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recommendations!