On the Estimation of Strong Means of Fourier Series - Pachulia, N. L. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
We study problem of (λ, φ) -strong summation of number series by the regular method λ with power summation of the function φ. The accumulated results are extended to the case of Fourier expansions in trigonometric functions f ϵ L_p, p > 1, where C is the set of 2π-periodic continuous functions. Some results are also obtained for the estimation of strong means of the method λ in L_p, p > 1, at the Lebesgue point x of the function f under certain additional conditions in the case where the function φ tends to infinity as u → ∞ faster than the exponential function (βu) − 1, β > 0.