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- W1566450047 abstract "Let $ellinmathbb{N}$ and $pin(1,infty]$. In this article, the authors prove that the sequence ${f-B_{ell,2^{-k}}f}_{kinmathbb{Z}}$ consisting of the differences between $f$ and the ball average $B_{ell,2^{-k}}f$ characterizes the Besov space $dot B^alpha_{p,q}(rn)$ with $qin (0, infty]$ and the Triebel-Lizorkin space $dot F^alpha_{p,q}(rn)$ with $qin (1,infty]$ when the smoothness order $alphain(0,2ell)$. More precisely, it is proved that $f-B_{ell,2^{-k}}f$ plays the same role as the approximation to the identity $varphi_{2^{-k}}ast f$ appearing in the definitions of $dot B^alpha_{p,q}(rn)$ and $dot F^alpha_{p,q}(rn)$. The corresponding results for inhomogeneous Besov and Triebel-Lizorkin spaces are also obtained. These results, for the first time, give a way to introduce Besov and Triebel-Lizorkin spaces with any smoothness order in $(0, 2ell)$ on spaces of homogeneous type, where $ellin{mathbb N}$." @default.
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- W1566450047 date "2015-07-28" @default.
- W1566450047 modified "2023-09-25" @default.
- W1566450047 title "Characterizations of Besov and Triebel-Lizorkin Spaces via Averages on Balls" @default.
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- W1566450047 doi "https://doi.org/10.48550/arxiv.1507.08004" @default.
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