On $T_{2n-1}^\perp$ spaces

TL;DR

This paper investigates inequalities for mean values of functions in $T_{2n-1}^ot$, providing simple proofs of classical inequalities and discussing sharp constants in Stechkin's inequality.

Contribution

It offers new estimates for mean values in $T_{2n-1}^ot$ and simplifies proofs of classical inequalities, advancing understanding of these function spaces.

Findings

Simplified proof of Jackson inequality for second modulus of continuity

New estimates for mean values in $T_{2n-1}^ot$

Discussion on sharp constants in Stechkin's inequality

Abstract

This paper is devoted to the inequalities for mean values of functions from $T_{2n-1}^\perp$. The simple proof of the classical Jackson inequality in the case of the second modulus of continuity may be considered as the consequence of our estimates. The problems of the sharp constants in classical Stechkin's inequality are also discussed.