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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
Abstract
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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- Copyright © Canadian Mathematical Society 1999