Estimates of best approximations of transformed Fourier series in $L^p$-norm and $p$-variational norm
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 1, pp. 111-126
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We consider functions $F=F(\lambda,f)$ with transformed Fourier series $\sum\limits^\infty_{n=1}\lambda_nA_n(x)$, where $\smash[t]{\sum\limits^\infty_{n=1}A_n(x)}$ is the Fourier series of a function $f$. Let $C_p$ be the space of $2\pi$-periodic $p$-absolutely continuous functions with $p$-variational norm. The estimates of best approximations of $F$ in $L^p$ in terms of best approximations of $f$ in $C_p$ are given. Also the dual problem for $F$ in $C_p$ and $f$ in $L^p$ is treated. In the important case of fractional derivative, the sharpness of estimates is established.
@article{FPM_2018_22_1_a5,
author = {S. S. Volosivets and A. A. Tyuleneva},
title = {Estimates of best approximations of transformed {Fourier} series in $L^p$-norm and $p$-variational norm},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {111--126},
publisher = {mathdoc},
volume = {22},
number = {1},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2018_22_1_a5/}
}
TY - JOUR AU - S. S. Volosivets AU - A. A. Tyuleneva TI - Estimates of best approximations of transformed Fourier series in $L^p$-norm and $p$-variational norm JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2018 SP - 111 EP - 126 VL - 22 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2018_22_1_a5/ LA - ru ID - FPM_2018_22_1_a5 ER -
%0 Journal Article %A S. S. Volosivets %A A. A. Tyuleneva %T Estimates of best approximations of transformed Fourier series in $L^p$-norm and $p$-variational norm %J Fundamentalʹnaâ i prikladnaâ matematika %D 2018 %P 111-126 %V 22 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2018_22_1_a5/ %G ru %F FPM_2018_22_1_a5
S. S. Volosivets; A. A. Tyuleneva. Estimates of best approximations of transformed Fourier series in $L^p$-norm and $p$-variational norm. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 1, pp. 111-126. http://geodesic.mathdoc.fr/item/FPM_2018_22_1_a5/