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Strong Converse Inequalities for Averages in Weighted L p Spaces on [-1,1]
Published online by Cambridge University Press: 20 November 2018
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.
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- Research Article
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- Copyright © Canadian Mathematical Society 1999
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