SL(n) covariant vector-valued valuations on Lp-spaces

被引：0
|
作者：
Wang, Wei [1 ]
He, Rigao [2 ]
Liu, Lijuan [1 ]
机构：
[1] Hunan Univ Sci & Technol, Sch Math & Computat Sci, Xiangtan 411201, Peoples R China
[2] Jiangxi Univ Sci & Technol, Dept Math, Ganzhou 341000, Jiangxi, Peoples R China
来源：
ANNALES MATHEMATIQUES DU QUEBEC | 2021年 / 45卷 / 02期
关键词：
Valuation; Moment vector; SL(n) covariance; TRANSLATION INVARIANT VALUATIONS; MINKOWSKI VALUATIONS; CONVEX-SETS; BODIES;
D O I：
10.1007/s40316-020-00153-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A complete classification of continuous SL(n) covariant vector-valued valuations on L-p(R-n, vertical bar x vertical bar dx) is obtained without any homogeneity assumptions. The moment vector is shown to be essentially the only such valuation.
引用
收藏
页码：465 / 486
页数：22
相关论文
共 50 条
  • [1] VECTOR-VALUED SCHRODINGER OPERATORS IN Lp-SPACES
    Kunze, Markus
    Maichine, Abdallah
    Rhandi, Abdelaziz
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2020, 13 (05): : 1529 - 1541
  • [2] Transference of Vector-valued Multipliers on Weighted LP-spaces
    Blasco, Oscar
    Villarroya, Paco
    [J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2013, 65 (03): : 510 - 543
  • [3] On weighted Lp-spaces of vector-valued entire analytic functions
    Joaquín Motos
    María Jesús Planells
    César F. Talavera
    [J]. Mathematische Zeitschrift, 2008, 260 : 451 - 472
  • [4] Vector-valued Fourier multipliers in Lp-spaces with power weights
    Pruess, Jan
    [J]. STUDIA MATHEMATICA, 2019, 247 (02) : 155 - 173
  • [5] On weighted Lp-spaces of vector-valued entire analytic functions
    Motos, Joaquin
    Planells, Maria Jesus
    Talavera, Cesar F.
    [J]. MATHEMATISCHE ZEITSCHRIFT, 2008, 260 (02) : 451 - 472
  • [6] A description of norm-convergent martingales on vector-valued LP-spaces
    Cullender, Stuart F.
    Labuschagne, Coenraad C. A.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (01) : 119 - 130
  • [7] The Bochner-Schoenberg-Eberlein Property for Vector-Valued lp-Spaces
    Kamali, Z.
    Abtahi, F.
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2020, 17 (03)
  • [8] An operator-valued transference principle and maximal regularity on vector-valued Lp-spaces
    Clément, P
    Prüss, J
    [J]. EVOLUTION EQUATIONS AND THEIR APPLICATIONS IN PHYSICAL AND LIFE SCIENCES, 2001, 215 : 67 - 87
  • [9] Valuations on Lp-Spaces
    Tsang, Andy
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (20) : 3993 - 4023
  • [10] SL(n)-covariant Lp-Minkowski valuations
    Parapatits, Lukas
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2014, 89 : 397 - 414
12345