Geodesic
Moduli of continuity and rearrangements
Matematičeskie zametki, Tome 18 (1975) no. 1, pp. 63-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that the modulus of continuity of a function in $L_p(0,1)$ majorizes the modulus of continuity of its decreasing rearrangement. 
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     author = {Yu. A. Brudnyi},
     title = {Moduli of continuity and rearrangements},
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Yu. A. Brudnyi. Moduli of continuity and rearrangements. Matematičeskie zametki, Tome 18 (1975) no. 1, pp. 63-66. http://geodesic.mathdoc.fr/item/MZM_1975_18_1_a8/