An estimate of an optimal argument in the sharp multidimensional Jackson–Stechkin $L_2$-inequality

D. V. Gorbachev

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 83-91

Résumé

An estimate of an optimal argument in the sharp Jackson–Stechkin inequality in the space $L_2(\mathbb R^n)$ is proved in the case of a generalized modulus of continuity; its special case is the classical modulus of continuity. Similar statements hold for the torus $\mathbb T^n$. The obtained results agree with Chernykh's classical one-dimensional theorems and refine some results by S. N. Vasil'ev, A. I. Kozko, and N. I. Rozhdestvenskii.

Détail

Keywords: best approximation, generalized modulus of continuity, sharp multidimensional Jackson–Stechkin inequality.

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