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, and let L_Ψ L_Ψ (T) = { f L_0(T) : \| f\| _Ψ := 12π _T Ψ (| f(x)| )dx < ∞ }. We study the properties of multiple modules of continuity for the functions from L_Ψ.