The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods applied to non-linear problems or for numerical approaches that make use of regularization techniques to cure low smoothness of the solution. This result is obtained through an estimate of the derivatives of composite functions in weighted uniform norm.

翻译：本文旨在给出加权空间中复合函数的最佳多项式逼近误差的特征描述。该特征对于非线性问题数值方法的收敛性分析，以及通过正则化技术处理解的低光滑性的数值方法至关重要。这一结果是通过对加权一致范数下复合函数导数的估计得到的。