1. CJM 1999 (vol 51 pp. 546)
|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