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Real Interpolation with Logarithmic Functors and Reiteration

Published online by Cambridge University Press:  20 November 2018

W. D. Evans  and
B. Opic
W. D. Evans
Affiliation:
School of Mathematics, Cardiff University, 23 Senghennydd Road, Cardiff CF24 4YH, United Kingdom email: Evanswd@cf.ac.uk
B. Opic
Affiliation:
Mathematical Institute of the Czech Academy of Sciences, Zitná 25, 115 67 Praha 1, Czech Republic email: opic@math.cas.cz
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Abstract

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We present “reiteration theorems” with limiting values $\theta =0$ and $\theta =1$ for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in $[\text{D}]$.

Keywords

46B7026D1046E30Real interpolationbroken-logarithmic functorsreiterationweighted inequalities
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 5 , 01 October 2000 , pp. 920 - 960
Copyright
Copyright © Canadian Mathematical Society 2000

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