Calderón couples of rearrangement invariant spaces
Studia Mathematica (1993)
- Volume: 106, Issue: 3, page 233-277
- ISSN: 0039-3223
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topKalton, 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
top- [1] J. Arazy and M. Cwikel, A new characterization of the interpolation spaces between and , Math. Scand. 55 (1984), 253-270. Zbl0571.46049
- [2] S. F. Bellenot, The Banach spaces of Maurey and Rosenthal and totally incomparable bases, J. Funct. Anal. 95 (1991), 96-105. Zbl0723.46001
- [3] S. F. Bellenot, R. Haydon and E. Odell, Quasi-reflexive and tree spaces constructed in the spirit of R. C. James, in: Contemp. Math. 85, Amer. Math. Soc., 1987, 19-43. Zbl0726.46005
- [4] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York 1988. Zbl0647.46057
- [5] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin 1976. Zbl0344.46071
- [6] N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge Univ. Press, 1987. Zbl0617.26001
- [7] Yu. Brudnyĭ and N. Kruglyak, Real interpolation functors, Soviet Math. Dokl. 23 (1981), 5-8. Zbl0475.46052
- [8] Yu. Brudnyĭ and N. Kruglyak, Interpolation Functors and Interpolation Spaces, North-Holland, 1991.
- [9] A. P. Calderón, Spaces between and and the theorems of Marcinkiewicz, Studia Math. 26 (1966), 273-299. Zbl0149.09203
- [10] P. G. Casazza, W. B. Johnson and L. Tzafriri, On Tsirelson's space, Israel J. Math. 47 (1984), 81-98.
- [11] P. G. Casazza and B. L. Lin, On symmetric basic sequences in Lorentz sequence spaces, II, ibid. 17 (1974), 191-218. Zbl0286.46019
- [12] P. G. Casazza and T. J. Shura, Tsirelson's space, Lecture Notes in Math. 1363, Springer, Berlin 1989. Zbl0709.46008
- [13] M. Cwikel, Monotonicity properties of interpolation spaces, Ark. Mat. 14 (1976), 213-236. Zbl0339.46024
- [14] M. Cwikel, Monotonicity properties of interpolation spaces II, ibid. 19 (1981), 123-136. Zbl0467.46061
- [15] M. Cwikel, K-divisibility of the K-functional and Calderón couples, ibid. 22 (1984), 39-62. Zbl0535.46049
- [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. Zbl0606.46050
- [17] M. Cwikel and P. Nilsson, Interpolation of Marcinkiewicz spaces, Math. Scand. 56 (1985), 29-42. Zbl0551.46052
- [18] M. Cwikel and P. Nilsson, Interpolation of weighted Banach lattices, Mem. Amer. Math. Soc., to appear. Zbl0548.46058
- [19] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1934.
- [20] F. L. Hernandez and B. Rodriguez-Salinas, On -complemented copies in Orlicz spaces II, Israel J. Math. 68 (1989), 27-55. Zbl0689.46006
- [21] P. W. Jones, On interpolation between and , 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. Zbl0329.46008
- [23] J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1971), 263-269. Zbl0211.16301
- [24] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, Berlin 1977. Zbl0362.46013
- [25] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, Berlin 1979. Zbl0403.46022
- [26] G. G. Lorentz, Relations between function spaces, Proc. Amer. Math. Soc. 12 (1961), 127-132.
- [27] G. G. Lorentz and T. Shimogaki, Interpolation theorems for the pairs of spaces and , Trans. Amer. Math. Soc. 159 (1971), 207-222.
- [28] L. Maligranda, On Orlicz results in interpolation theory, in: Proc. Orlicz Memorial Conference, Univ. of Mississippi, 1990. Zbl0760.46058
- [29] L. Maligranda and V. I. Ovchinnikov, On interpolation between and , J. Funct. Anal. 107 (1992), 342-351.
- [30] C. Merucci, Interpolation réelle avec fonction paramètre: réitération et applications aux espaces , C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 427-430. Zbl0504.46055
- [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).
- [33] S. J. Montgomery-Smith, Comparison of Orlicz-Lorentz spaces, Studia Math. 103 (1992), 161-189. Zbl0814.46023
- [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). Zbl0253.46080
- [36] G. Sparr, Interpolation of weighted -spaces, Studia Math. 62 (1978), 229-271. Zbl0393.46029
- [37] B. S. Tsirelson, Not every Banach space contains an embedding of or , Functional Anal. Appl. 8 (1974), 138-141.
- [38] Q. Xu, Notes on interpolation of Hardy spaces, Ann. Inst. Fourier (Grenoble) 42 (1992), 877-889. Zbl0760.46060
- [39] M. Zippin, On perfectly homogeneous bases in Banach spaces, Israel J. Math. 4 (1966), 265-272. Zbl0148.11202
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