On the optimal constants in the two-sided Stechkin inequalities
Abstract
We address the optimal constants in the strong and the weak Stechkin inequalities, both in their discrete and continuous variants. These inequalities appear in the characterization of approximation spaces which arise from sparse approximation or have applications to interpolation theory. An elementary proof of a constant in the strong discrete Stechkin inequality given by Bennett is provided, and we improve the constants given by Levin and Stechkin and by Copson. Finally, the minimal constants in the weak discrete Stechkin inequalities and both continuous Stechkin inequalities are presented.
Cite
@article{arxiv.2006.07441,
title = {On the optimal constants in the two-sided Stechkin inequalities},
author = {Thomas Jahn and Tino Ullrich},
journal= {arXiv preprint arXiv:2006.07441},
year = {2021}
}
Comments
v2: adds the continuous inequalities and acknowledgments, v3: corrects typos in authors' addresses and enhances acknowledgments, v4: introduces major rework in Section 2, minor rework in all other parts, v4: corrects typos