On the rate of convergence for the Chebyshev series

Let f(x) be a function of bounded variation on [-1,1] and S _n(f;x) the nth partial sum of the expansion of f(x) in a Chebyshev series of the second kind. In this note we give the estimate for the rate of convergence of the sequence S_n(f;x) to f(x) in terms of the modulus of continuity of the total variation of f(x).