Approximation by convolution operators. (English) Zbl 0907.41012
Proceedings of the 3rd international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, September 23–28, 1996. Vols. I and II. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 52, 523-536 (1998).
Authors’ abstract: As a result the best lower estimate for certain convolution operators are given, for the de la Vallée-Poussin operator, and especially for the (classical) Jackson operator \(J_{n,2}\). For this operator we use a different approach and obtain for every \(1\leq p\leq \infty\)
\[
C^{-1} K_2\left(f,{1 \over n}\right)_p \leq \| f-J_{n,2} f\|_p.
\]
For the entire collection see [Zbl 0892.00039].
For the entire collection see [Zbl 0892.00039].
Reviewer: D.Braess (Bochum)
MSC:
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
