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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.

##### MSC:
 42A10 Trigonometric approximation
Full Text:
##### References:
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