Geodesic
A new function space and applications
Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2083-2101.

Voir la notice de l'article provenant de la source EMS Press

We define a new function space B, which contains in particular BMO, BV, and W1/p,p, 1∞. We investigate its embedding into Lebesgue and Marcinkiewicz spaces. We present several inequalities involving Lp norms of integer-valued functions in B. We introduce a significant closed subspace, B0​, of B, containing in particular VMO and W1/p,p, 1≤p∞. The above mentioned estimates imply in particular that integer-valued functions belonging to B0​ are necessarily constant. This framework provides a "common roof" to various, seemingly unrelated, statements asserting that integer-valued functions satisfying some kind of regularity condition must be constant.
DOI : 10.4171/jems/551
Classification : 46-XX
Keywords: BMO, VMO, BV, Sobolev spaces, integer-valued functions, constant function, isoperimetric inequality 
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Jean Bourgain; Haïm Brezis; Petru Mironescu. A new function space and applications. Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2083-2101. doi : 10.4171/jems/551. http://geodesic.mathdoc.fr/articles/10.4171/jems/551/

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