In the recent literature certain BMO-type seminorms provide characterizations of Sobolev functions. In the same order of ideas, we obtain the norm of the gradient of a function in Lp(Ω), where Ω⊂Rn, n>1 and p>1, as limit of BMO-type seminorms involving families of pairwise disjoint sets with all orientations, the sets being not necessarily cubes or tessellation cells. An analogous result is obtained when rotations are not allowed.
BMO-type seminorms generating Sobolev functions / Farroni, F.; Guarino Lo Bianco, S.; Schiattarella, R.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 491:1(2020), p. 124298. [10.1016/j.jmaa.2020.124298]
BMO-type seminorms generating Sobolev functions
Guarino Lo Bianco S.;
2020
Abstract
In the recent literature certain BMO-type seminorms provide characterizations of Sobolev functions. In the same order of ideas, we obtain the norm of the gradient of a function in Lp(Ω), where Ω⊂Rn, n>1 and p>1, as limit of BMO-type seminorms involving families of pairwise disjoint sets with all orientations, the sets being not necessarily cubes or tessellation cells. An analogous result is obtained when rotations are not allowed.
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