Littlewood–Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 104-118
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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.
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
@article{10_4153_CMB_2015_038_9,
author = {He, Ziyi and Yang, Dachun and Yuan, Wen},
title = {Littlewood{\textendash}Paley {Characterizations} of {Second-Order} {Sobolev} {Spaces} via {Averages} on {Balls}},
journal = {Canadian mathematical bulletin},
pages = {104--118},
year = {2016},
volume = {59},
number = {1},
doi = {10.4153/CMB-2015-038-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-038-9/}
}
TY - JOUR AU - He, Ziyi AU - Yang, Dachun AU - Yuan, Wen TI - Littlewood–Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls JO - Canadian mathematical bulletin PY - 2016 SP - 104 EP - 118 VL - 59 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-038-9/ DO - 10.4153/CMB-2015-038-9 ID - 10_4153_CMB_2015_038_9 ER -
%0 Journal Article %A He, Ziyi %A Yang, Dachun %A Yuan, Wen %T Littlewood–Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls %J Canadian mathematical bulletin %D 2016 %P 104-118 %V 59 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-038-9/ %R 10.4153/CMB-2015-038-9 %F 10_4153_CMB_2015_038_9
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