Pointwise characterizations of Besov and Triebel-Lizorkin spaces in terms of averages on balls

Yang, Dachun; Yuan, Wen

doi:10.1090/tran/6871

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.

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