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Strong Converse Inequalities for Averages in Weighted $L^p$ Spaces on $[-1,1]$ |
Canad. J. Math. 51(1999), 546-565
Published:1999-06-01
Printed: Jun 1999
Printed: Jun 1999
- M. Felten
Abstract
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 |
| MSC Classifications: |
41A25 - Rate of convergence, degree of approximation 41A63 - Multidimensional problems (should also be assigned at least one other classification number in this section) |