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.

引用

页数：28

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