Geodesic
A Sharp Jackson Inequality in $L_p(\mathbb R^d)$ with Dunkl Weight
Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 666-684

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A sharp Jackson inequality in the space $L_p(\mathbb R^d)$, $1\le p2$, with Dunkl weight is proved. The best approximation is realized by entire functions of exponential spherical type. The modulus of continuity is defined by means of a generalized shift operator bounded on $L_p$, which was constructed earlier by the authors. In the case of the unit weight, this operator coincides with the mean-value operator on the sphere.
Keywords: Dunkl transform, best approximation, generalized shift operator, modulus of continuity, Jackson inequality. 
@article{MZM_2019_105_5_a2,
     author = {D. V. Gorbachev and V. I. Ivanov},
     title = {A {Sharp} {Jackson} {Inequality} in $L_p(\mathbb R^d)$ with {Dunkl} {Weight}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {666--684},
     publisher = {mathdoc},
     volume = {105},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a2/}
}
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D. V. Gorbachev; V. I. Ivanov. A Sharp Jackson Inequality in $L_p(\mathbb R^d)$ with Dunkl Weight. Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 666-684. http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a2/