Geodesic
Best Approximation and Symmetric Decreasing Rearrangements of Functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 179-193

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The problem of estimating the best approximation by a subspace of classes of functions of $n$ variables defined by restrictions imposed on the modulus of continuity is considered on the basis of the duality principle. An approach is analyzed that is connected with the representation of a function of $n$ variables as a countable sum of simple functions and the subsequent transition to spatial symmetric decreasing rearrangements. 
@article{TM_2001_232_a15,
     author = {N. P. Korneichuk},
     title = {Best {Approximation} and {Symmetric} {Decreasing} {Rearrangements} of {Functions}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {179--193},
     publisher = {mathdoc},
     volume = {232},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_232_a15/}
}
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N. P. Korneichuk. Best Approximation and Symmetric Decreasing Rearrangements of Functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 179-193. http://geodesic.mathdoc.fr/item/TM_2001_232_a15/