On a certain norm and related applications
Let \(QC(\mathbb{T})\) be the closure of trigonometrical polynomials with respect to the norm \[ \|f\|_{QC}:= \int^1_0 \Biggl\|\sum^\infty_{k=0} r_k(\omega) \sum_{2^{k-1}\leq |n|< 2^k}\widehat f(n)e^{inx}\Biggr\|_{L_\infty(\mathbb{T})}d\omega, \] where \(\{r_k(\omega)\}^\infty_{k= 0}\) is the Rademacher system. Using this and norms closed to it, the authors accounce several inequalities for trigonometric polynomials and their applications to in order sharp estimates of entropy numbers and Kolmogorov width.
scientific article; zbMATH DE number 1294965
scientific article