Average Nikolskii factors for random trigonometric polynomials
Abstract
For $1\le p,q\le \infty $, the Nikolskii factor for a trigonometric polynomial $T_{{\mathbf{a}}}$ is defined by $$ N_{p,q}(T_{{\mathbf{a}}})= \frac{\|T_{{\mathbf{a}}}\|_{q}}{\|T_{{\mathbf{a}}}\|_{p}},\ \ T_{{ \mathbf{a}}}(x)=a_{1}+\sum \limits ^{n}_{k=1}(a_{2k}\sqrt{2}\cos kx+a_{2k+1} \sqrt{2}\sin kx). $$ We study this average Nikolskii factor for random trigonometric polynomials with independent $N(0,\sigma ^{2})$ coefficients and obtain the exact orders. For $1\leq p< q
Fields of Study & Subjects
Geometry and complex manifolds
Mathematical functions and polynomials
Holomorphic and Operator Theory
Publication details
- Journal / source
- Journal of Inequalities and Applications
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 1
- Publication date
- 27 April 2026
- Language
- EN