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Trigonometric approximation of functions in $L _{p}$-norm. (English) Zbl 1011.42001
This is a very nice paper. The author investigates trigonometric polynomials associated with $f\in \text{Lip}(\alpha, p)$ ($0<\alpha\le 1$, $p\ge 1$) to approximate $f$ in $L_p$-norm to the degree of $O(n^{-\alpha})$ $(0<\alpha\le 1)$. The most interesting results treat the case $\alpha= 1$. His three new theorems have numerous attractive corollaries, some of them give sharper estimates than the known ones.

42A10Trigonometric approximation
Full Text: DOI
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[2] Chandra, P.: Functions of classes lp and lip({$\alpha$},p) and their Riesz means. Riv. mat. Univ. parma (4) 12, 275-282 (1986) · Zbl 0642.41014
[3] Chandra, P.: A note on degree of approximation by nörlund and Riesz operators. Mat. vestnik 42, 9-10 (1990) · Zbl 0725.42004
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