Geodesic
Littlewood–Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 104-118

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, the authors characterize second-order Sobolev spaces ${{W}^{2,p}}({{\mathbb{R}}^{n}})$ , with $p\,\in \,[2,\,\infty )$ and $n\,\in \,\mathbb{N}\,\text{or}\,p\,\in \,(1,\,2)\,\text{and}\,n\,\in \,\left\{ 1,\,2,\,3 \right\}$ , via the Lusin area function and the Littlewood–Paley $g_{\text{ }\!\!\lambda\!\!\text{ }}^{*}$ -function in terms of ball means.
DOI : 10.4153/CMB-2015-038-9
Mots-clés : 46E35, 42B25, 42B20, 42B35, Sobolev space, ball means, Lusin-area function, g*λ-function 
He, Ziyi; Yang, Dachun; Yuan, Wen. Littlewood–Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls. Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 104-118. doi: 10.4153/CMB-2015-038-9
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