Lipschitz and Triebel-Lizorkin spaces associated with the Dunkl operators on Rd

被引：0
|
作者：
Kallel, Samir [1 ,2 ]
机构：
[1] Univ Tunis El Manar, Fac Sci Tunis, Lab Anal Math & Applicat LR11ES11, El Manar 1, Tunis 2092, Tunisia
[2] Monastir Univ, Higher Inst Comp Sci & Math Monastir, Dept Math, Monastir 5000, Tunisia
来源：
POSITIVITY | 2019年 / 23卷 / 05期
关键词：
Dunkl operators; Dunkl-Poisson transforms; Dunkl-Lipschitz spaces; Dunkl-Triebel-Lizorkin spaces; Dunkl-Flett potentials; BESOV-SPACES; TEMPERATURES; POTENTIALS;
D O I：
10.1007/s11117-019-00650-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we define Lipschitz and Triebel-Lizorkin spaces associated with the differential-difference Dunkl operators on Rd. We study inclusion relations among them. Next, some interpolation results and continuity results of some important operators (the Dunkl-Poisson semigroup and Dunkl-Flett potentials) on them are established. Also, we prove certain inclusion relations between Dunkl-Sobolev classes L alpha,kp(R-d) of positive fractional order alpha, Dunkl-Lipschitz spaces perpendicular to alpha,p,qk(R-d) and Dunkl-Triebel-Lizorkin spaces F alpha,p,qk(R-d).
引用
收藏
页码：1021 / 1049
页数：29
相关论文
共 50 条
  • [1] Lipschitz and Triebel-Lizorkin spaces, commutators in Dunkl setting
    Han, Yongsheng
    Lee, Ming-Yi
    Li, Ji
    Wick, Brett D.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2023, 237
  • [2] ON DILATION OPERATORS IN TRIEBEL-LIZORKIN SPACES
    Schneider, Cornelia
    Vybral, Jan
    [J]. FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2009, 41 (02) : 139 - 162
  • [3] Besov and Triebel-Lizorkin Spaces Associated to Hermite Operators
    The Anh Bui
    Xuan Thinh Duong
    [J]. Journal of Fourier Analysis and Applications, 2015, 21 : 405 - 448
  • [4] Duals of Besov and Triebel-Lizorkin Spaces Associated with Operators
    Georgiadis, Athanasios G.
    Kyriazis, George
    [J]. CONSTRUCTIVE APPROXIMATION, 2023, 57 (02) : 547 - 577
  • [5] Besov and Triebel-Lizorkin Spaces Associated to Hermite Operators
    The Anh Bui
    Xuan Thinh Duong
    [J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2015, 21 (02) : 405 - 448
  • [6] Duals of Besov and Triebel-Lizorkin Spaces Associated with Operators
    Athanasios G. Georgiadis
    George Kyriazis
    [J]. Constructive Approximation, 2023, 57 : 547 - 577
  • [7] Embeddings between Triebel-Lizorkin Spaces on Metric Spaces Associated with Operators
    Georgiadis, Athanasios G.
    Kyriazis, George
    [J]. ANALYSIS AND GEOMETRY IN METRIC SPACES, 2020, 8 (01): : 418 - 429
  • [8] Continuity of multilinear operators on Triebel-Lizorkin spaces
    Lanzhe Liu
    [J]. Journal of Inequalities and Applications, 2006
  • [9] Continuity of multilinear operators on Triebel-Lizorkin spaces
    Liu, Lanzhe
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2006, 2006 (1)
  • [10] WEIGHTED BESOV AND TRIEBEL-LIZORKIN SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS
    Huy-Qui Bui
    The Anh Bui
    Xuan Thinh Duong
    [J]. FORUM OF MATHEMATICS SIGMA, 2020, 8
12345