On the norm of the hyperinterpolation operator on the unit ball

We obtain the asymptotic order of the operator norm of the hyperinterpolation operator on the unit ball Bd,d≥2 with respect to the measure bd,μ(1−∣x∣2)μ−1/2dx,μ≥0, where bd,μ=(∫Bd(1−∣x∣2)μ−1/2dx)−1bd,μ=(∫Bd(1−∣x∣2)μ−1/2dx)−1.