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 Fundam. Prikl. Mat., 2018, Volume 22, Issue 1, Pages 111–126 (Mi fpm1783)

Estimates of best approximations of transformed Fourier series in $L^p$-norm and $p$-variational norm

S. S. Volosivets, A. A. Tyuleneva

Saratov State University

Abstract: 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.

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Citation: S. S. Volosivets, A. A. Tyuleneva, “Estimates of best approximations of transformed Fourier series in $L^p$-norm and $p$-variational norm”, Fundam. Prikl. Mat., 22:1 (2018), 111–126

Citation in format AMSBIB
\Bibitem{VolTyu18} \by S.~S.~Volosivets, A.~A.~Tyuleneva \paper Estimates of best approximations of transformed Fourier series in $L^p$-norm and $p$-variational norm \jour Fundam. Prikl. Mat. \yr 2018 \vol 22 \issue 1 \pages 111--126 \mathnet{http://mi.mathnet.ru/fpm1783}