Limiting variants of Krasnoselʼskiĭʼs compact interpolation theorem

We illustrate how limiting variants of Krasnoselʼskiĭʼs compact interpolation theorem may be obtained. As a special case of our results it follows that compactness is preserved on certain Lorentz–Zygmund spaces close to the end-point Lebesgue spaces.

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Bibliographic Details
Published in:Journal of functional analysis 2014-03, Vol.266 (5), p.3265-3285
Main Authors: Edmunds, David E., Opic, Bohumír
Format: Article
Language:English
Subjects:
Compact operators
Interpolation
K-functional
Lebesgue spaces
Lorentz–Zygmund spaces
Type of interpolation method
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Description
Summary:We illustrate how limiting variants of Krasnoselʼskiĭʼs compact interpolation theorem may be obtained. As a special case of our results it follows that compactness is preserved on certain Lorentz–Zygmund spaces close to the end-point Lebesgue spaces.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2013.10.029