Rational approximation to functions like \(x^{\alpha}\) in integral norms
The main result of the paper concerns the degree of rational approximation in the Hardy space \(H^ p\) of functions that are of Markov-Stieltjes type with special conditions on the measures. As a consequence known estimates for the degree of rational approximation to \(x^{\alpha}\) in \(L^ p[0,1]\), \(1<p<\infty\), for rational \(\alpha\) are extended to hold also for \(\alpha\) irrational. The case when \(\alpha\) is rational was studied by Vjacheslavov and (for \(p=\infty)\) by Ganelius.
scientific article; zbMATH DE number 4065589