Pointwise characterizations of Besov and Triebel-Lizorkin spaces in terms of averages on balls
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- by Dachun Yang and Wen Yuan PDF
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Abstract:
In this article, the authors characterize Besov spaces $\dot B^{\alpha }_{p,q}(\mathbb {R}^n)$ and Triebel-Lizorkin spaces $\dot F^{\alpha }_{p,q}(\mathbb {R}^n)$ with $\alpha \in (0,\infty )$, $p\in (1,\infty ]$ and $q\in (0,\infty ]$ ($q\in (1,\infty ]$ for $F$ spaces), as well as their inhomogeneous versions, via some pointwise inequalities involving ball averages. These pointwise characterizations provide a way to introduce Besov and Triebel-Lizorkin spaces with arbitrary positive smoothness on metric measure spaces.References
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Additional Information
- Dachun Yang
- Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China
- MR Author ID: 317762
- Email: dcyang@bnu.edu.cn
- Wen Yuan
- Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China
- MR Author ID: 743517
- Email: wenyuan@bnu.edu.cn
- Received by editor(s): June 6, 2015
- Received by editor(s) in revised form: October 22, 2015
- Published electronically: April 11, 2017
- Additional Notes: This project was supported by the National Natural Science Foundation of China (Grant Nos. 11571039 and 11471042), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120003110003) and the Fundamental Research Funds for Central Universities of China (Grant No. 2014KJJCA10).
The second author is the corresponding author. - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 7631-7655
- MSC (2010): Primary 46E35; Secondary 42B25, 42B35
- DOI: https://doi.org/10.1090/tran/6871
- MathSciNet review: 3695840