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Strong Converse Inequalities for Averages in Weighted Lp Spaces on [-1,1]

Published online by Cambridge University Press:  20 November 2018

M. Felten
M. Felten*
Affiliation:
Universität Dortmund, Mathematik VIII, D-44221 Dortmund, Germany email: felten@zx2.hrz.uni-dortmund.de
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Abstract

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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.

Keywords

41A2541A63averagesK-functionalsweighted spacesstrong converse inequalities
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 3 , 01 June 1999 , pp. 546 - 565
Copyright
Copyright © Canadian Mathematical Society 1999

References

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