Hankel operators and the Dixmier trace on the Hardy space

被引：8
|
作者：
Englis, Miroslav [1 ,2 ]
Zhang, Genkai [3 ]
机构：
[1] Silesian Univ, Math Inst, Rybnicku 1, Opava 74601, Czech Republic
[2] Czech Acad Sci, Math Inst, Zitna 25, Prague 11567 1, Czech Republic
[3] Chalmers TH Goteborg Univ, Dept Math Sci, SE-41296 Gothenburg, Sweden
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2016年 / 94卷
关键词：
INTERPOLATION;
D O I：
10.1112/jlms/jdw037
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there exist Dixmier-class Hankel operators that are not measurable (that is, their Dixmier trace depends on the choice of the underlying Banach limit), as well as Dixmier-class Hankel operators that do not belong to the Schatten-Lorentz ideal. A related question concerning logarithmic interpolation of Besov spaces is also discussed.
引用
收藏
页码：337 / 356
页数：20
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