Geodesic
Jackson inequality in $L_2(\mathbb T^N)$ with generalized modulus of continuity
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 102-110

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The sharp Jackson inequality is proved for the space of periodic functions of many variables with mean-square norm for an arbitrary modulus of continuity generated by a difference operator with constant coefficients.
Keywords: Jackson inequality, generalized modulus of continuity, multidimensional approximation. 
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S. N. Vasil'ev. Jackson inequality in $L_2(\mathbb T^N)$ with generalized modulus of continuity. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 102-110. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a7/