Pachulia N. L.
Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 809–819
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 $\exp (βu) − 1, β > 0$.
Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1103-1111
In the metric of L, we obtain estimates for the generalized means of deviations of partial Fourier sums from an arbitrary summable function in terms of the corresponding means of its best approximations by trigonometric polynomials.
Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 545-555
Uniform estimates of the integral strong mean deviations of continuous functions by entire functions
Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 235-241
Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1434–1441
Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 808-814
Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 101-105