Geodesic
The multidimensional Jackson theorem in $L_p$
Matematičeskie zametki, Tome 52 (1992) no. 1, pp. 105-113.

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This article considers the best approximation of a periodic function of several real variables by trigonometric polynomials with hyperbolic-cross harmonics. Theorems are proved on upper bounds for the indicated best approximation in terms of the modulus of continuity of the given function. 
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     author = {N. N. Pustovoitov},
     title = {The multidimensional {Jackson} theorem in $L_p$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {105--113},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1992_52_1_a14/}
}
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N. N. Pustovoitov. The multidimensional Jackson theorem in $L_p$. Matematičeskie zametki, Tome 52 (1992) no. 1, pp. 105-113. http://geodesic.mathdoc.fr/item/MZM_1992_52_1_a14/