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Complex interpolation and Calderón product of quasi-Banach spaces |
Wen YUAN() |
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
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Abstract We prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calderón product. This generalizes a classical result by V. A. Shestakov in 1974 for Banach lattices.
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Keywords
Complex interpolation
Calderón product
quasi-Banach lattice
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Corresponding Author(s):
Wen YUAN
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Issue Date: 17 May 2016
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Calderón A P. Intermediate spaces and interpolation, the complex method. Studia Math, 1964, 24: 113–190
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2 |
Janson S. Minimal and maximal methods of interpolation. J Funct Anal, 1981, 44: 50–73
https://doi.org/10.1016/0022-1236(81)90004-5
|
3 |
Kalton N. Plurisubharmonic functions on quasi-Banach spaces. Studia Math, 1986, 84: 297–324
|
4 |
Kalton N, Mayboroda S, Mitrea M. Interpolation of Hardy-Sobolev-Besov-Triebel-Lizorkin spaces and applications to problems in partial differential equations. In: De Carli L, Milman M, eds. Interpolation Theory and Applications. Contemp Math, Vol 445. Providence: Amer Math Soc, 2007, 121–177
https://doi.org/10.1090/conm/445/08598
|
5 |
Kalton N, Mitrea M. Stability results on interpolation scales of quasi-Banach spaces and applications. Trans Amer Math Soc, 1998, 350: 3903–3922
https://doi.org/10.1090/S0002-9947-98-02008-X
|
6 |
Lu Y, Yang D, Yuan W. Interpolation of Morrey spaces on metric measure spaces. Canad Math Bull, 2014, 57: 598–608
https://doi.org/10.4153/CMB-2013-009-4
|
7 |
Nilsson P. Interpolation of Banach lattices. Studia Math, 1985, 82: 133–154
|
8 |
Peetre J. Sur l’utilisation des suites inconditionellement sommables dans la théorie des espaces d’interpolation. Rend Sem Mat Univ Padova, 1971, 46: 173–190
|
9 |
Shestakov V A. Interpolation of linear operators in spaces of measurable functions. Funktsional Anal i Prilozhen, 1974, 8: 91–92 (in Russian)
|
10 |
Shestakov V A. On complex interpolation of Banach spaces of measurable functions. Vestnik Leningrad Univ, 1974, 19: 64–68 (in Russian)
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11 |
Yuan W, Sickel W, Yang D. Interpolation of Morrey-Campanato and related smoothness spaces. Sci China Math, 2015, 58: 1835–1908
https://doi.org/10.1007/s11425-015-5047-8
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