Geodesic
Variation Reducing Properties of Decreasing Rearrangements
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 330-336

Voir la notice de l'article provenant de la source Cambridge University Press

One well-established characteristic of the operation of decreasing rearrangement is its variation reducing property. A systematic study of this property has been made in considerable detail by G.F.D. Duff in [5] and [6]. He proved some inequalities related to the operation of rearrangement in decreasing order showing that the total variation of a sequence or an absolutely continuous function is in general diminished by such rearrangement. He also showed that the Lp norm of the difference sequence (or the derivative function) is diminished by this rearrangement operation unless the given sequence (or absolutely continuous function) is already monotonie (or equal to a monotonie function almost everywhere). 
Chong, Kong-Ming. Variation Reducing Properties of Decreasing Rearrangements. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 330-336. doi: 10.4153/CJM-1975-040-2
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