Some Estimates for the Error of Best Polynomial Approximation of Composite Functions

The purpose of the paper is to provide upper estimates of the error of best polynomial approximation of composite functions in weighted spaces. Such estimates are essential for the convergence analysis of numerical methods applied to non-linear problems or for numerical approaches making use of regularization techniques to cure the low smoothness of the solution. These results are obtained through a suitable estimate of the derivatives of composite functions in $L^p$ and uniform weighted norms.