Variable exponent Besov-Lipschitz and Triebel-Lizorkin spaces for the Gaussian measure

被引：1
作者：
Pineda, Ebner [1 ]
Rodriguez, Luz [1 ]
Urbina, Wilfredo [2 ]
机构：
[1] Escuela Super Politecn Litoral ESPOL, Fac Ciencias Nat & Matemat, Dept Matemat, Campus Gustavo Galindo km 30-5 Vıa Perimetra, EC-090112 Guayaquil, Ecuador
[2] Roosevelt Univ, Dept Math & Actuarial Sci, Chicago, IL 60605 USA
来源：
AIMS MATHEMATICS | 2023年 / 8卷 / 11期
关键词：
Ornstein-Uhlenbeck; variable exponent; Besov-Lipschitz; Triebel-Lizorkin; Gaussian measure;
D O I：
10.3934/math.20231388
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce variable Gaussian Besov-Lipschitz B alpha p(center dot),q(center dot)(gamma d) and TriebelLizorkin spaces F alpha p(center dot),q(center dot)(gamma d), i.e., Gaussian Besov-Lipschitz and Triebel-Lizorkin spaces with variable exponents p(center dot) and q(center dot), under certain regularity conditions on the functions p(center dot) and q(center dot). The condition on p(center dot) is associated with the Gaussian measure and was introduced in [3]. Trivially, they include the Gaussian Besov-Lipschitz B alpha p,q(gamma d) and Triebel-Lizorkin spaces F alpha p,q(gamma d) for p,qconstants, which were introduced and studied in [10]. We consider some inclusion relations of those spaces and finally prove some interpolation results for them.
引用
收藏
页码：27128 / 27150
页数：23
相关论文
共 23 条
[1]   New diffusion models in image processing [J].
Aboulaich, R. ;
Meskine, D. ;
Souissi, A. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (04) :874-882
[2]  
[Anonymous], 1992, II. Monogr. Math.
[3]  
CruzUribe DV, 2013, APPL NUMER HARMON AN, DOI 10.1007/978-3-0348-0548-3
[4]   Riesz transforms on variable Lebesgue spaces with Gaussian measure [J].
Dalmasso, Estefania ;
Scotto, Roberto .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2017, 28 (05) :403-420
[5]  
Diening L., 2007, Fract. Calc. Appl. Anal., V10
[6]   Lebesgue and Sobolev Spaces with Variable Exponents [J].
Diening, Lars ;
Harjulehto, Petteri ;
Hasto, Peter ;
Ruzicka, Michael .
LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+
[7]   Variable Triebel-Lizorkin-Type Spaces [J].
Drihem, Douadi .
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (02) :1817-1856
[8]  
Gatto A. E., 2013, Springer Proceedings in Mathematics and Statistics, V25, P105, DOI [10.1007/978-1-4614-4565-4, DOI 10.1007/978-1-4614-4565-4]
[9]  
Moreno Jorge, 2021, Rev.colomb.mat., V55, P21
[10]  
Pineda E, 2022, Arxiv, DOI [arXiv:2205.11752, 10.48550/arXiv.2205.11752, DOI 10.48550/ARXIV.2205.11752]
123