Continuity moduli of functions from Waterman classes (Q1276024)

The author treats the class of functions \(f(x)\) with period 1 which have the Waterman \(\Lambda\)-bounded variation. For such functions boundedness conditions are established for the integral moduli of continuity \((p\geq 1)\) \[ \omega(f,\delta)_p = \sup_{| t| \leq \delta}\left(\int_{I} | f([x,x+t])| ^p dx\right)^{\frac 1p}. \]