Estimating Dixmier traces of Hankel operators in Lorentz ideals

被引：1
|
作者：
Goffeng, Magnus [1 ,2 ]
Usachev, Alexandr [3 ]
机构：
[1] Chalmers Univ Technol, Dept Math Sci, SE-41296 Gothenburg, Sweden
[2] Univ Gothenburg, SE-41296 Gothenburg, Sweden
[3] Cent South Univ, Sch Math & Stat, Changsha 410085, Hunan, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 279卷 / 07期
基金：
瑞典研究理事会;
关键词：
Hankel operator; Hardy space; Dixmier trace; Besov space;
D O I：
10.1016/j.jfa.2020.108688
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study Dixmier traces of powers of Hankel operators in Lorentz ideals. We extend results of Englis-Zhang to the case of powers p >= 1 and general Lorentz ideals starting from abstract extrapolation results of Gayral-Sukochev. In the special case p = 2, 4, 6 we give an exact formula for the Dixmier trace. For general p, we give upper and lower bounds on the Dixmier trace. We also construct, for any p and any Lorentz ideal, examples of non-measurable Hankel operators. (C) 2020 Elsevier Inc. All rights reserved.
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页数：28
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