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 \(f\in \text{Lip}(\alpha, p)\) (\(0<\alpha\leq 1\), \(p\geq 1\)) to approximate \(f\) in \(L_p\)-norm to the degree of \(O(n^{-\alpha})\) \((0<\alpha\leq 1)\). 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.


42A10 Trigonometric approximation
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