Calderón couples of rearrangement invariant spaces

N. Kalton

Studia Mathematica (1993)

  • Volume: 106, Issue: 3, page 233-277
  • ISSN: 0039-3223

Abstract

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We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with L . 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 ) forms a Calderón pair.

How to cite

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Kalton, N.. "Calderón couples of rearrangement invariant spaces." Studia Mathematica 106.3 (1993): 233-277. <http://eudml.org/doc/216016>.

@article{Kalton1993,
abstract = {We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with $L_∞.$ 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 $(L_F,L_∞)$ forms a Calderón pair.},
author = {Kalton, N.},
journal = {Studia Mathematica},
keywords = {rearrangement invariant function spaces; Calderón couple; Orlicz spaces},
language = {eng},
number = {3},
pages = {233-277},
title = {Calderón couples of rearrangement invariant spaces},
url = {http://eudml.org/doc/216016},
volume = {106},
year = {1993},
}

TY - JOUR
AU - Kalton, N.
TI - Calderón couples of rearrangement invariant spaces
JO - Studia Mathematica
PY - 1993
VL - 106
IS - 3
SP - 233
EP - 277
AB - We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with $L_∞.$ 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 $(L_F,L_∞)$ forms a Calderón pair.
LA - eng
KW - rearrangement invariant function spaces; Calderón couple; Orlicz spaces
UR - http://eudml.org/doc/216016
ER -

References

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