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1. CJM 1999 (vol 51 pp. 546)
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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 Categories:41A25, 41A63 |