средние Валле–Пуссена

Variable exponent p(x) Lebesgue spaces L^p(x)_2π is considered. For f ∈ L^p(x)_2π Vallee–Poussin means Vⁿ_m(f, x) can be defined as Vⁿ_m(f, x) = 1/(m+1)Ʃ_l=0^mS_n+l(f, x), where Sk(f, x) –- partial Fourier sum of f(x) of order k. Approximative properties of operators Vⁿ_m(f) = Vⁿ_m(f, x) are investigated in L^p(x)_2π. Let p(x) ≥ 1 be 2π-periodical variable exponent that satisfies Dini–Lipschitz condition.