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

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


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 $L_{\Psi}$.
How to Cite
Pichugov, S. 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,
Research articles