TY - JOUR
AU - N. L. Pachulia
PY - 2015/06/25
Y2 - 2024/03/05
TI - On the Estimation of Strong Means of Fourier Series
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 6
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2023
AB - 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 $\exp (βu) − 1, β > 0$.
ER -