@article{Bustamante_2023, title={New estimates related with the best polynomial approximation}, volume={52}, url={https://ictp.acad.ro/jnaat/journal/article/view/1313}, DOI={10.33993/jnaat521-1313}, abstractNote={<p>In some old results, we find estimates the best approximation \(E_{n,p}(f)\) of a periodic function satisfying \(f^{(r)}\in\mathbb{L}^p_{2\pi}\) in terms of the norm of \(f^{(r)}\) (Favard inequality). In this work, we look for a similar result under the weaker assumption \(f^{(r)}\in \mathbb{L}^q_{2\pi}\), with \(1&lt;q&lt;p&lt;\infty\). We will present inequalities of the form \(E_{n,p}(f)\leq C(n)\Vert D^{(r)}f\Vert_q\), where \(D^{(r)}\) is a differential operator. We also study the same problem in spaces of non-periodic functions with a Jacobi weight.</p>}, number={1}, journal={J. Numer. Anal. Approx. Theory}, author={Bustamante, Jorge}, year={2023}, month={Jul.}, pages={75–81} }