The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Canadian Journal of Mathematics
( Vol. 51 NO.3 / (1999))
Strong Converse Inequalities for Averages in Weighted $L^p$ Spaces on [-1,1]
M. Felten,
Pages. 546-565
Abstract Averages in weighted spaces $L_phi^p[-1,1]$ 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.
Contents 1. Introduction
2. Preliminary considerations
3. Properties of averages
4. The direct result
5. Strong converse inequalities of types A and B
6. Strong converse inequalities of type D
Key words $K$-functionals, weighted spaces, strong converse inequalities
Mathmatical Subject Classification 41A25, 41A63