Approximation properties of combination of multivariate averages on Hardy spaces. (English) Zbl 1377.41004
For distributions \(f\), belonging to the Hardy space \(H^p(\mathbb{R}^n)\), some combination \( \mathfrak{J}_{l,t}^\beta (f) \) of multivariate averages are introduced. For \(\beta =0\), they coincide with known averages that are studied by F. Dai and Z. Ditzian [J. Approx. Theory 131, No. 2, 268–283 (2004; Zbl 1109.41010)]. The problem of the equivalence of deviation \(||\mathfrak{J}_{l,t}^\beta (f)-f||_{H^p( \mathbb{R}^n)}\) and \(K\)-functionals, constructed with the help of Riesz potential, are considered. The main attention is paid to the case \(0<p\leq 1\), but the evidence is valid for \(1<p<\infty \).
Reviewer: D. K. Ugulawa (Tbilisi)
MSC:
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
| 41A63 | Multidimensional problems |
| 42B30 | \(H^p\)-spaces |
Citations:
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