Geodesic
Strong Converse Inequalities for Averages in Weighted L p Spaces on [-1,1]
Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 546-565

Voir la notice de l'article provenant de la source Cambridge University Press

Averages in weighted spaces $L_{\phi }^{p}[-1,1]$ defined by additions on $[-1,\,1]$ will be shown to satisfy strong converse inequalities of type $\text{A}$ and $\text{B}$ with appropriate $K$ -functionals. Results for higher levels of smoothness are achieved by combinations of averages. This yields, in particular, strong converse inequalities of type $\text{D}$ between $K$ -functionals and suitable difference operators.
DOI : 10.4153/CJM-1999-025-7
Mots-clés : 41A25, 41A63, averages, K-functionals, weighted spaces, strong converse inequalities 
Felten, M. Strong Converse Inequalities for Averages in Weighted L p Spaces on [-1,1]. Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 546-565. doi: 10.4153/CJM-1999-025-7
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[Di-Fe] [Di-Fe] Ditzian, Z. andFelten, M., Averages using translation induced by Laguerre and Jacobi expansions. Constr. Approx., to appear. Google Scholar

[Di-Iv] [Di-Iv] Ditzian, Z. and Ivanov, K., Strong converse inequalities. J. Anal. Math.. 61 (1993), 61–111. Google Scholar

[Di-Ru] [Di-Ru] Ditzian, Z. and Runovskii, K., Averages and K-functionals related to the Laplacian. J. Approx. Theory, to appear. Google Scholar

[Fe1] [Fe1] Felten, M., A Smoothness Concept forWeighted Lp Spaces on[−1; 1] Acta Sci.Math.. 62 (1996), 217–230. Google Scholar

[Fe2] [Fe2] Felten, M., A modulus of smoothness based on an algebraic addition. Aequationes Math.. 54 (1997), 56–73. Google Scholar

[Fe3] [Fe3] Felten, M., Characterization of best algebraic approximation by an algebraic modulus of smoothness. J. Approx. Theory. 89 (1997), 1–25. Google Scholar

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