Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight

A generalized modulus of continuity is defined in the space $L_2(\mathbb R^d)$ with Dunkl weight by means of an arbitrary zero-sum sequence of complex numbers. A sharp generalized Jackson inequality is proved for this modulus and the best approximations by entire functions of exponential spherical type. This inequality was earlier proved by S. N. Vasil'ev in the weightless case.