Bounds from below and diameters of classes of periodic functions with a bounded fractional derivative
Using the notations of the paper the main result reads as follows: Let \(\alpha \in {\mathfrak R}\), \(r \geq 1\) and \(m \leq C \cdot (r + 1)\). Then \[ d_{2m -1} (W_ \infty^{r, \alpha})_ \infty = d_{2m}(W_ \infty^{r,\alpha})_ \infty = d_{2m - 1} (W_ 1^{r,\alpha})_ 1 = {4 \over \pi m^ r} M_{r,\alpha}. \]
scientific article; zbMATH DE number 567885
scientific article