A Sharp Jackson Inequality in Lp(ℝd) with Dunkl Weight

详细

A sharp Jackson inequality in the space L_p(ℝ^d), 1 ≤ p < 2, 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.