Inverse Jackson theorems in spaces with integral metric

  • S. A. Pichugov Днепропетр. нац. ун-т ж.-д. трансп.

Abstract

In the spaces $L_{\Psi}(T)$ of periodic functions with metric $\rho(f, 0)_{\Psi} = \int_T \Psi(|f(x)|)dx$, where $\Psi$ is a function of the modulus-of-continuity type, we investigate the inverse Jackson theorems in the case of approximation by trigonometric polynomials. It is proved that the inverse Jackson theorem is true if and only if the lower dilation exponent of the function $\Psi$ is not equal to zero.
Published
25.03.2012
How to Cite
PichugovS. A. “Inverse Jackson Theorems in Spaces With Integral Metric”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 3, Mar. 2012, pp. 351-62, http://umj.imath.kiev.ua/index.php/umj/article/view/2581.
Section
Research articles