Complex interpolation functors with a family of quasi-power function parameters

Ming Fan

Studia Mathematica (1994)

  • Volume: 111, Issue: 3, page 283-305
  • ISSN: 0039-3223

Abstract

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For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskiĭ construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters which are quasi-powers with a logarithmic factor.

How to cite

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Fan, Ming. "Complex interpolation functors with a family of quasi-power function parameters." Studia Mathematica 111.3 (1994): 283-305. <http://eudml.org/doc/216133>.

@article{Fan1994,
abstract = {For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskiĭ construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters which are quasi-powers with a logarithmic factor.},
author = {Fan, Ming},
journal = {Studia Mathematica},
keywords = {complex interpolation functors associated with derivatives of analytic functions; Calderón fundamental inequality; discretization; reiteration; Calderón-Lozanovskij construction for Banach lattices; Aronszajn-Gagliardo construction concerning minimality and maximality},
language = {eng},
number = {3},
pages = {283-305},
title = {Complex interpolation functors with a family of quasi-power function parameters},
url = {http://eudml.org/doc/216133},
volume = {111},
year = {1994},
}

TY - JOUR
AU - Fan, Ming
TI - Complex interpolation functors with a family of quasi-power function parameters
JO - Studia Mathematica
PY - 1994
VL - 111
IS - 3
SP - 283
EP - 305
AB - For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskiĭ construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters which are quasi-powers with a logarithmic factor.
LA - eng
KW - complex interpolation functors associated with derivatives of analytic functions; Calderón fundamental inequality; discretization; reiteration; Calderón-Lozanovskij construction for Banach lattices; Aronszajn-Gagliardo construction concerning minimality and maximality
UR - http://eudml.org/doc/216133
ER -

References

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  2. [BK] Yu. A. Brudnyĭ and N. Ya. Kruglyak, Interpolation Functors and Interpolation Spaces, North-Holland, Amsterdam, 1991. 
  3. [BL] J. Bergh and J. Löfström, Interpolation Spaces, Grundlehren Math. Wiss. 223, Springer, Berlin, 1976. Zbl0344.46071
  4. [Cal] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190. Zbl0204.13703
  5. [CC] M. J. Carro and J. Cerdà, Complex interpolation and L p -spaces, ibid. 99 (1991), 57-67. 
  6. [CCS] M. J. Carro, J. Cerdà and J. Sueiro, On Fourier type and uniform convexity of interpolated spaces, Boll. Un. Mat. Ital. 3 (1989), 883-899. Zbl0711.46055
  7. [Cw] M. Cwikel, Complex interpolation spaces, a disrete definition and reiteration, Indian J. Math. 27 (1978), 1005-1009. Zbl0409.46067
  8. [FK] M. Fan and S. Kaijser, Complex interpolation with derivatives of analytic functions, J. Funct. Anal. 120 (1994), 380-402. Zbl0806.46077
  9. [G] J. Gustavsson, Interpolation of weighted L p -spaces, Studia Math. 72 (1982), 237-251. Zbl0497.46051
  10. [GP] J. Gustavsson and J. Peetre, Interpolation of Orlicz spaces, ibid. 60 (1977), 33-59. Zbl0353.46019
  11. [J] S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 14 (1981), 50-72. Zbl0492.46059
  12. [KP] S. Kaijser and J. W. Pelletier, Interpolation Functors and Duality, Lecture Notes in Math. 1208, Springer, Berlin, 1986. 
  13. [KMP] N. Ya. Kruglyak, L. Maligranda and L. E. Persson, A Carlson type inequality with blocks and interpolation, Studia Math. 104 (1993), 161-180. Zbl0824.46088
  14. [N] P. Nilsson, Interpolation of Banach lattices, ibid. 82 (1985), 135-154. Zbl0549.46038
  15. [Pee] J. Peetre, H ∞ and complex interpolation, Technical report, Univ. of Lund, 1981. 
  16. [Per] L. E. Persson, Interpolation with a parameter function, Math. Scand. 59 (1986), 199-222. Zbl0619.46064
  17. [S] M. Schechter, Complex interpolation, Compositio Math. 18 (1967), 117-147. Zbl0153.16402

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