Abstract
We obtain a new characterization of the higher Sobolev space \(W^{m,p}(\mathbb R^{n})\), \(m\in \mathbb N\) and \(p\in (1, +\infty )\) and of the space BVm, the space of functions of higher order bounded variation. The characterizations are in term of BMO-type seminorms. The results unify and substantially extend previous results in Fusco et al. (ESAIM Control Optim. Calc Var., 24(2), 835–847 2018) and Farroni et al. (J. Funct. Anal., 278(9), 108451 2020).
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23 July 2022
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Open access funding provided by Università degli Studi di Napoli Federico II within the CRUI-CARE Agreement. The authors are members of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of INdAM. The research of S.G.L.B. has been funded by PRIN Project 2017AYM8XW and the research of R.S. has been funded by PRIN Project 2017JFFHSH.
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Bianco, S.G.L., Schiattarella, R. A BMO-Type Characterization of Higher Order Sobolev Spaces. Potential Anal 59, 917–932 (2023). https://doi.org/10.1007/s11118-022-09987-8
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DOI: https://doi.org/10.1007/s11118-022-09987-8