On mean convergence of Hermite-Fejér interpolation (Q1911359)

If \(H_n (f, x)\) is the Hermite-Fejér interpolation polynomial of the function \(f\) based on the zeros of the Chebyshev polynomial and if \[ |f|_{w,2}= \Biggl( \int^1_{-1} {1\over {\sqrt {1-x^2}}} |f(x) |^2 dx \Biggr)^{1/2} \] then for each polynomial \(f\neq \text{const.}\), \(|H_n (f, x)- f(x) |_{w,2} \sim 1/n\).