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Zbl 1050.41014
Belinsky, E.; Dai, F.; Ditzian, Z.
Multivariate approximating averages. (English)
[J] J. Approximation Theory 125, No. 1, 85-105 (2003). ISSN 0021-9045

Summary: Averages on the sphere about $x$ in $R^d$ and on the rim of the cap about $x$ in $S^{d-1}$ and their iterates are shown to be smoother than $f$. Furthermore, their approximating properties satisfy a strong converse inequality of type $A$ when dealing with multivariate approximation ($d \geqslant 2$ in case of $R^d$ and $d \geqslant 3$ in case of $S^{d-1}$). These results are in contrast to the classical results on $R$ or $T$ for which the situation is completely different.

MSC 2000:: *41A25 Degree of approximation, etc.
41A63 Multidimensional approximation problems
42B15 Multipliers, several variables

Keywords: Moduli of smoothness; Strong converse inequality; Smoothness of an averaging operator; Multipliers

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Zentralblatt MATH Berlin [Germany]