On $T_{2n-1}^\perp$ spaces
  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. 
A.G. Babenko, Yu.Kryakin