Search: All articles in the CJM digital archive with keyword $K$-functionals
 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 inequalitiesCategories:41A25, 41A63