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Calder\'on couples of re-arrangement invariant spaces

Nigel J. Kalton
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Abstract

We examine conditions under which a pair of re-arrangement invariant function spaces on $[0,1]$ or $[0,\infty)$ form a Calder\'on couple. A very general criterion is developed to determine whether such a pair is a Calder\'on couple, with numerous applications. We give, for example, a complete classification of those spaces $X$ which form a Calder\'on couple with $L_{\infty}.$ We specialize our results to Orlicz spaces and are able to give necessary and sufficient conditions on an Orlicz function $F$ so that the pair $(L_F,L_{\infty})$ forms a Calder\'on pair.

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Nigel J. Kalton. 1992-09-25. Calder\'on couples of re-arrangement invariant spaces. https://arxiv.org/abs/math/9209217

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