Some properties of the moduli of continuity of periodic functions in metric spaces

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

Abstract

Let $L_0(T)$) be the set of real-valued periodic measurable functions, let $\Psi : R^{+} \rightarrow R^{+}$ be the modulus of continuity, and let $$L_{\Psi} \equiv L_{\Psi} (T) = \left\{ f \in L_0(T) : \| f\| _{\Psi} := \frac1{2\pi} \int_T \Psi (| f(x)| )dx < \infty \right\}.$$ We study the properties of multiple modules of continuity for the functions from $L_{\Psi}$.
Published
25.12.2016
How to Cite
PichugovS. A. “Some Properties of the Moduli of Continuity of Periodic Functions in Metric Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 12, Dec. 2016, pp. 1657-64, http://umj.imath.kiev.ua/index.php/umj/article/view/1951.
Section
Research articles