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Strong Converse Inequalities for Averages in Weighted $L^p$ Spaces on $[-1,1]$

  Published:1999-06-01
 Printed: Jun 1999
  • M. Felten
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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 averages, $K$-functionals, weighted spaces, strong converse inequalities
MSC Classifications: 41A25, 41A63 show english descriptions Rate of convergence, degree of approximation
Multidimensional problems (should also be assigned at least one other classification number in this section)
41A25 - Rate of convergence, degree of approximation
41A63 - Multidimensional problems (should also be assigned at least one other classification number in this section)
 

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