Geodesic
Characterizations of Besov-Type and Triebel–Lizorkin–Type Spaces via Averages on Balls
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 655-672

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DOI

Let $\ell \in \mathbb{N}$ and $\alpha \in (0,2\ell )$ . In this article, the authors establish equivalent characterizations of Besov-type spaces, Triebel–Lizorkin-type spaces, and Besov–Morrey spaces via the sequence ${{\{f-{{B}_{\ell ,{{2}^{-k}}}}f\}}_{k}}$ consisting of the difference between $f$ and the ball average ${{B}_{\ell ,{{2}^{-k}}}}f$ . These results lead to the introduction of Besov-type spaces, Triebel–Lizorkin-type spaces, and Besov–Morrey spaceswith any positive smoothness order onmetricmeasure spaces. As special cases, the authors obtain a new characterization of Morrey–Sobolev spaces and ${{\text{Q}}_{\alpha }}$ spaces with $\alpha \in (0,1)$ , which are of independent interest.
DOI : 10.4153/CMB-2016-076-7
Mots-clés : 42B25, 46E35, 42B35, Besov space, Triebel–Lizorkin space, ball average, Calderón reproducing formula 
Zhuo, Ciqiang; Sickel, Winfried; Yang, Dachun; Yuan, Wen. Characterizations of Besov-Type and Triebel–Lizorkin–Type Spaces via Averages on Balls. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 655-672. doi: 10.4153/CMB-2016-076-7
@article{10_4153_CMB_2016_076_7,
     author = {Zhuo, Ciqiang and Sickel, Winfried and Yang, Dachun and Yuan, Wen},
     title = {Characterizations of {Besov-Type} and {Triebel{\textendash}Lizorkin{\textendash}Type} {Spaces} via {Averages} on {Balls}},
     journal = {Canadian mathematical bulletin},
     pages = {655--672},
     year = {2017},
     volume = {60},
     number = {3},
     doi = {10.4153/CMB-2016-076-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-076-7/}
}
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%J Canadian mathematical bulletin
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