Toeplitz operators on Bergman spaces of polygonal domains. Issue 4 (26th June 2019)

• Record Type: Journal Article
• Authors: Mannersalo, Paula
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 62:Issue 4(2019)
• Page Start: 1115
• Page End: 1136
• Publication Date: 2019-06-26
• Subjects: Toeplitz operator, -- Bergman space, -- boundedness, -- polygonal domain, -- locally integrable symbol, -- Whitney decomposition, -- Schwarz–Christoffel formula; Primary 47B35; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091519000105
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: We study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces A p (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 A p (Ω) in the case where polygon Ω has such a large corner that the Bergman projection is unbounded.