On functions of bounded p-variation

We obtain estimates of the total p-variation ( 1 < p < ∞ ) and other related functionals for a periodic function f ∈ L p [ 0 , 1 ] in terms of its L p -modulus of continuity ω ( f ; δ ) p . These estimates are sharp for any rate of the decay of ω ( f ; δ ) p . Moreover, the constant coefficients in them depend on parameters in an optimal way.