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 B d , d 2 with respect to the measure b d , µ ( 1 - x 2 ) µ - 1 / 2 d x , µ 0 , where b d , µ = ( B d ( 1 - x 2 ) µ - 1 / 2 d x ) - 1 .