Geodesic
Estimates of the~best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the~multidimensional Jackson's theorem
Sbornik. Mathematics, Tome 188 (1997) no. 10, pp. 1507-1520

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In the first section the best approximations of periodic functions of one real variable by trigonometric polynomials are studied. Estimates of these approximations in terms of averaged differences are obtained. A multidimensional generalization of these estimates is presented in the second section. As a consequence. The multidimensional Jackson's theorem is proved. 
@article{SM_1997_188_10_a3,
     author = {N. N. Pustovoitov},
     title = {Estimates of the~best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the~multidimensional {Jackson's} theorem},
     journal = {Sbornik. Mathematics},
     pages = {1507--1520},
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     volume = {188},
     number = {10},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_10_a3/}
}
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N. N. Pustovoitov. Estimates of the~best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the~multidimensional Jackson's theorem. Sbornik. Mathematics, Tome 188 (1997) no. 10, pp. 1507-1520. http://geodesic.mathdoc.fr/item/SM_1997_188_10_a3/