Geodesic
A new function space and applications
Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2083-2101 Cet article a éte moissonné depuis la source EMS Press

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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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     author = {Jean Bourgain and Ha{\"\i}m Brezis and Petru Mironescu},
     title = {A new function space and applications},
     journal = {Journal of the European Mathematical Society},
     pages = {2083--2101},
     year = {2015},
     volume = {17},
     number = {9},
     doi = {10.4171/jems/551},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/551/}
}
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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

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