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# Strong Converse Inequalities for Averages in Weighted $L^p$ Spaces on $[-1,1]$

Averages in weighted spaces $L^p_\phi[-1,1]$ defined by additions on $[-1,1]$ will be shown to satisfy strong converse inequalities of type A and 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 D between $K$-functionals and suitable difference operators.
 Keywords: averages, $K$-functionals, weighted spaces, strong converse inequalities