Besov-type and Triebel–Lizorkin-type spaces associated with heat kernels
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- 作者：Liguang Liu ; Dachun Yang ; Wen Yuan
- 关键词：Besov space ; Triebel–Lizorkin space ; Metric measure space ; Heat kernel ; Peetre maximal function ; Frame
- 刊名：Collectanea Mathematica
- 出版年：2016
- 出版时间：May 2016
- 年：2016
- 卷：67
- 期：2
- 页码：247-310
- 全文大小：1,182 KB
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Dachun Yang (3)
Wen Yuan (3)
1. Department of Mathematics, School of Information, Renmin University of China, Beijing, 100872, China
2. Department of Mathematics, University of Bielefeld, 33501, Bielefeld, Germany
3. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Algebra
Analysis
Applications of Mathematics
Geometry - 出版者：Springer Milan
- ISSN：2038-4815
文摘
Let \((M, \rho ,\mu )\) be a space of homogeneous type satisfying the reverse doubling condition and the non-collapsing condition. In this paper, the authors introduce Besov-type spaces \(B_{p,q}^{s,\tau }(M)\) and Triebel–Lizorkin-type spaces \(F_{p,q}^{s,\tau }(M)\) associated to a nonnegative self-adjoint operator \(L\) whose heat kernel satisfies sub-Gaussian upper bound estimate, Hölder continuity, and stochastic completeness. The novelty in this article is that the indices \(p,q,s,\tau \) here can be take full range of all possible values as in the Euclidean setting. Characterizations of these spaces via Peetre maximal functions and the heat semigroup are established for full range of possible indices. Also, frame characterizations of these spaces are given. When \(L\) is the Laplacian operator on \(\mathbb R^n\), these spaces coincide with the Besov-type and Triebel–Lizorkin-type spaces on \(\mathbb R^n\) studied in (Yuan et al. Lecture Notes in Mathematics, vol 2005, 2010). In the case \(\tau =0\) and the smoothness index \(s\) is around zero, comparisons of these spaces with the Besov and Triebel–Lizorkin spaces studied in (Han et al. Abstr Appl Anal 1–250, 2008, Art ID 893409) are also presented.