On the connection between the real and the complex interpolation method for several Banach spaces

J. I. Bertolo; D. L. Fernandez

Rendiconti del Seminario Matematico della Università di Padova (1982)

  • Volume: 66, page 193-209
  • ISSN: 0041-8994

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Bertolo, J. I., and Fernandez, D. L.. "On the connection between the real and the complex interpolation method for several Banach spaces." Rendiconti del Seminario Matematico della Università di Padova 66 (1982): 193-209. <http://eudml.org/doc/107841>.

@article{Bertolo1982,
author = {Bertolo, J. I., Fernandez, D. L.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {connections between the real and the complex interpolation method; Lions- Peetre interpolation method; multiple Poisson integrals},
language = {eng},
pages = {193-209},
publisher = {Seminario Matematico of the University of Padua},
title = {On the connection between the real and the complex interpolation method for several Banach spaces},
url = {http://eudml.org/doc/107841},
volume = {66},
year = {1982},
}

TY - JOUR
AU - Bertolo, J. I.
AU - Fernandez, D. L.
TI - On the connection between the real and the complex interpolation method for several Banach spaces
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1982
PB - Seminario Matematico of the University of Padua
VL - 66
SP - 193
EP - 209
LA - eng
KW - connections between the real and the complex interpolation method; Lions- Peetre interpolation method; multiple Poisson integrals
UR - http://eudml.org/doc/107841
ER -

References

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  1. [1] A. Benedek - R. Panzone, The spaces Lp, with mixed norm, Duke Math. J., 28 (1961), pp. 301-324. Zbl0107.08902MR126155
  2. [2] A.P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), pp. 113-190. Zbl0204.13703MR167830
  3. [3] A. Favini, Su una estensione del metodo d'interpolazione complesso, Rend. Sem. Mat. Univ. Padova, 47 (1972), pp. 244-298. Zbl0248.46032MR324439
  4. [4] D.L. Fernandez, Interpolation of 2n-tuples of Banach spaces, Studia Math., 65 (1979), pp. 87-113. Zbl0462.46051MR557490
  5. [5] D.L. Fernandez, An extension of the complex method of interpolation, Boll. U.M.I., 18-B (1981), pp. 721-732. Zbl0481.46033MR641731
  6. [6] D.L. Fernandez, On the interpolation of 2n Banach espaces - I: The Lions-Peetre interpolation method, Bull. Inst. Polytech. Iasi (to appear). Zbl0517.46052
  7. [7] J.L. Lions, Une construction d'espaces d'interpolation, C. R. Acad. Sci. Paris, 251 (1960), pp. 1853-1855. Zbl0118.10702MR119093
  8. [8] J.L. Lions - J. Peetre, Sur une classe d'espaces d'interpolation, Pub. Math. de l'IHES, 19 (1964). Zbl0148.11403
  9. [9] P.I. Lizorkin, Generalized Liouville differentiation and the functional space Lnp(En). Imbedding theorems, Math. Sb., 60 (102) (1963), pp. 325-353. Zbl0134.31703MR150615
  10. [10] P.I. Lizorkin - S.M. Nikols'kii, A classification of differentiable functions in some fundamental space with mixed derivetives, Proc. Steklov Inst. Mat., 77 (1967), pp. 160-187. Zbl0165.47201
  11. [11] S.M. Nikols'kii, Functions with dominant mixed derivatives satisfying a multiple Hölder condition, AMS transl., 2 (102) (1973), pp. 27-51. Zbl0271.46027
  12. [12] J. Peetre, Sur le nombre de paramètres dans la définition de certains espaces d'interpolation, Ric. Mat., 12 (1963), pp. 248-261. Zbl0125.06501MR169043
  13. [13] J. Peetre, Sur le transformation de Fourier des fonctions à valeurs vectorielles, Rend. Sem. Mat. Univ. Padova, 42 (1969), pp. 15-26. Zbl0241.46033MR256153
  14. [14] G. Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl., 99 (1974), pp. 247-316. Zbl0282.46022MR372641
  15. [15] A. Yoshikawa, Sur la théorie d'espaces d'interpolation: les espaces de moyenne de plusieurs espaces de Banach, J. Fac. Sc. Univ. Tokyo, 16 (1970), pp. 407-468. Zbl0197.09901MR634085

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