We obtain a new characterization of the higher Sobolev space Wm,p(Rn), m ∈ N and p ∈ (1,+∞) and of the space BV m, 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).
A BMO-Type Characterization of Higher Order Sobolev Spaces / Guarino Lo Bianco, S.; Schiattarella, R.. - In: POTENTIAL ANALYSIS. - ISSN 1572-929X. - 59:3(2023), pp. 917-932. [10.1007/s11118-022-09987-8]
A BMO-Type Characterization of Higher Order Sobolev Spaces
Guarino Lo Bianco S.;Schiattarella R.
2023
Abstract
We obtain a new characterization of the higher Sobolev space Wm,p(Rn), m ∈ N and p ∈ (1,+∞) and of the space BV m, 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).File in questo prodotto:
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