On best polynomial approximation in \(L_ w^ 2 (S)\) (Q1910837)

The best polynomial approximation is estimated by appropriate \(K\)-functionals in \(L^2_w (S)\) where \(w(x)\) is a Jacobi-type weight and \(S\) is a simplex (or prism). For \(L^p_w [-1, 1]\) the best polynomial approximation will be estimated for \(w_\lambda (x)= (1- x^2 )^{\lambda- 1/2}\) and \((2\lambda+ 1)/ (\lambda+ 1)< p< (2\lambda+ 1)/\lambda\).