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1993 | 106 | 3 | 233-277
Tytuł artykułu

Calderón couples of rearrangement invariant spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
106
Numer
3
Strony
233-277
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-10-27
Twórcy
autor
  • Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, U.S.A.
Bibliografia
  • [1] J. Arazy and M. Cwikel, A new characterization of the interpolation spaces between $L_p$ and $L_q$, Math. Scand. 55 (1984), 253-270.
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  • [15] M. Cwikel, K-divisibility of the K-functional and Calderón couples, ibid. 22 (1984), 39-62.
  • [16] M. Cwikel and P. Nilsson, On Calderón-Mityagin couples of Banach lattices, in: Proc. Conf. Constructive Theory of Functions, Varna 1984, Bulgarian Acad. Sci., 1984, 232-236.
  • [17] M. Cwikel and P. Nilsson, Interpolation of Marcinkiewicz spaces, Math. Scand. 56 (1985), 29-42.
  • [18] M. Cwikel and P. Nilsson, Interpolation of weighted Banach lattices, Mem. Amer. Math. Soc., to appear.
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  • [21] P. W. Jones, On interpolation between $H_1$ and $H_∞$, in: Interpolation Spaces and Allied Topics in Analysis, Proc. Lund Conference 1983, M. Cwikel and J. Peetre (eds.), Lecture Notes in Math. 1070, Springer, 1984, 143-151.
  • [22] J. L. Krivine, Sous espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. 104 (1976), 1-29.
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  • [30] C. Merucci, Interpolation réelle avec fonction paramètre: réitération et applications aux espaces $Λ^p(ϕ) (0 < p ℓ + ∞)$, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 427-430.
  • [31] C. Merucci, Applications of interpolation with a function parameter to Lorentz, Sobolev and Besov spaces, in: Interpolation Spaces and Allied Topics in Analysis, Proc. Lund Conference 1983, M. Cwikel and J. Peetre (eds.), Lecture Notes in Math. 1070, Springer, 1984, 183-201.
  • [32] B. S. Mityagin, An interpolation theorem for modular spaces, Mat. Sb. 66 (1965), 473-482 (in Russian).
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  • [34] V. I. Ovchinnikov, On the estimates of interpolation orbits, Mat. Sb. 115 (1981), 642-652 (in Russian) (= Math. USSR-Sb. 43 (1982), 573-583).
  • [35] A. A. Sedaev and E. M. Semenov, On the possibility of describing interpolation spaces in terms of Peetre's K-method, Optimizatsiya 4 (1971), 98-114 (in Russian).
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Bibliografia
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