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Approximation of a class of singular integrals by algebraic polynomials with regard to the location of a point on an interval. (English. Russian original) Zbl 1005.41002
Function spaces, harmonic analysis, and differential equations. Collected papers. Dedicated to the 95th anniversary of academician S. M. Nikol’skii. Transl. from the Russian. Moscow: MAIK Nauka/Interperiodika Publishing, Proc. Steklov Inst. Math. 232, 260-277 (2001); translation from Tr. Mat. Inst. Steklova 232, 268-285 (2001).
The author proves a sharp version of a S. Nikolskij-A. Timan type result for the class
$$W^r_\infty H^\omega[-1,1]$$ of $$r$$-differentiable functions satisfying $|f^{(r)}(x)- f^{(r)}(y)|\leq \omega(|x- y|).$ Here $$\omega$$ is assumed to be concave and such that $$\omega(0)= 0$$ and $$t\omega'(t)$$ is nondecreasing.
For the entire collection see [Zbl 0981.00017].

MSC:
 41A10 Approximation by polynomials 41A35 Approximation by operators (in particular, by integral operators) 65D30 Numerical integration