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# Real Interpolation with Logarithmic Functors and Reiteration

Published:2000-10-01
Printed: Oct 2000
• W. D. Evans
• B. Opic
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## Abstract

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 [D].
 Keywords: real interpolation, broken-logarithmic functors, reiteration, weighted inequalities
 MSC Classifications: 46B70 - Interpolation between normed linear spaces [See also 46M35] 26D10 - Inequalities involving derivatives and differential and integral operators 46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)