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
收藏
页数：28
相关论文
共 50 条
  • [31] Dixmier traces on noncompact isospectral deformations
    Gayral, Victor
    Iochum, Bruno
    Varilly, Joseph C.
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 237 (02) : 507 - 539
  • [32] The effect of boundary geometry on Hankel operators belonging to the trace ideals of Bergman spaces
    Krantz, SG
    Li, SY
    Rochberg, R
    [J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1997, 28 (02) : 196 - 213
  • [33] The effect of boundary geometry on Hankel operators belonging to the trace ideals of Bergman spaces
    Steven G. Krantz
    Song-Ying Li
    Richard Rochberg
    [J]. Integral Equations and Operator Theory, 1997, 28 : 196 - 213
  • [34] Hankel operators, the Segal-Bargmann space, and symmetrically-normed ideals
    Farnsworth, Duane
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 260 (05) : 1523 - 1542
  • [35] Representations Connected with Dixmier Traces and Spaces of Distributions
    R. S. Ismagilov
    [J]. Acta Applicandae Mathematica, 2004, 81 : 121 - 127
  • [36] Discrete analogues of Dixmier operators
    Mironov, A. E.
    [J]. SBORNIK MATHEMATICS, 2007, 198 (9-10) : 1433 - 1442
  • [37] Lidskii-Type Formulae for Dixmier Traces
    Sedaev, A. A.
    Sukochev, F. A.
    Zanin, D. V.
    [J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2010, 68 (04) : 551 - 572
  • [38] Hankel operators and Hankel algebras
    Yan, SZ
    Chen, XM
    Guo, KY
    [J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 1998, 19 (01) : 65 - 76
  • [39] HANKEL OPERATORS AND HANKEL ALGEBRAS
    Y AN S HAOZONG * C HEN X IAOMAN * G UO K UNYU *
    [J]. Chinese Annals of Mathematics,Series B, 1998, (01) : 65 - 76
  • [40] Lidskii-Type Formulae for Dixmier Traces
    A. A. Sedaev
    F. A. Sukochev
    D. V. Zanin
    [J]. Integral Equations and Operator Theory, 2010, 68 : 551 - 572
12345