TOEPLITZ OPERATORS ON BERGMAN SPACES OF POLYGONAL DOMAINS

被引：2

作者：

Mannersalo, Paula ^{[1
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, POB 68, FI-00014 Helsinki, Finland

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2019年 / 62卷 / 04期

关键词：

Toeplitz operator; Bergman space; boundedness; polygonal domain; locally integrable symbol; Whitney decomposition; Schwarz-Christoffel formula; PROJECTIONS;

D O I：

10.1017/S0013091519000105

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces A(p)(Omega), 1 < p < infinity, where Omega subset of 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 Omega in the proof. We also give examples of bounded Toeplitz operators on A(p)(Omega) in the case where polygon Omega has such a large corner that the Bergman projection is unbounded.

引用

页码：1115 / 1136

页数：22

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