Some properties of the moduli of continuity of periodic functions in metric spaces - Pichugov, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
Let $L_0(T)$) be the set of real-valued periodic measurable functions, let $Ψ : R^{+} → R^{+}$ be the modulus of continuity, andlet$$L_{Ψ} \equiv L_{Ψ} (T) =\left\{ f \in L_0(T) : \| f\| _{Ψ} := \frac1{2π} \int_T Ψ (| f(x)| )dx < ∞ \right\}.$$We study the properties of multiple modules of continuity for the functions from $L_{Ψ}$.