Reiteration and a Wolff theorem for interpolation methods defined by means of polygons

Fernando Cobos; Pedro Fernandez-Martinez

Studia Mathematica (1992)

  • Volume: 102, Issue: 3, page 239-256
  • ISSN: 0039-3223

Abstract

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We prove a reiteration theorem for interpolationmethods defined by means of polygons, and a Wolff theorem for the case when the polygon has 3 or 4 vertices. In particular, we establish a Wolff theorem for Fernandez' spaces, which settles a problem left over in [5].

How to cite

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Cobos, Fernando, and Fernandez-Martinez, Pedro. "Reiteration and a Wolff theorem for interpolation methods defined by means of polygons." Studia Mathematica 102.3 (1992): 239-256. <http://eudml.org/doc/215926>.

@article{Cobos1992,
abstract = {We prove a reiteration theorem for interpolationmethods defined by means of polygons, and a Wolff theorem for the case when the polygon has 3 or 4 vertices. In particular, we establish a Wolff theorem for Fernandez' spaces, which settles a problem left over in [5].},
author = {Cobos, Fernando, Fernandez-Martinez, Pedro},
journal = {Studia Mathematica},
keywords = {reiteration theorem; interpolation; means of polygons; Wolff theorem; Fernandez' spaces},
language = {eng},
number = {3},
pages = {239-256},
title = {Reiteration and a Wolff theorem for interpolation methods defined by means of polygons},
url = {http://eudml.org/doc/215926},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Cobos, Fernando
AU - Fernandez-Martinez, Pedro
TI - Reiteration and a Wolff theorem for interpolation methods defined by means of polygons
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 3
SP - 239
EP - 256
AB - We prove a reiteration theorem for interpolationmethods defined by means of polygons, and a Wolff theorem for the case when the polygon has 3 or 4 vertices. In particular, we establish a Wolff theorem for Fernandez' spaces, which settles a problem left over in [5].
LA - eng
KW - reiteration theorem; interpolation; means of polygons; Wolff theorem; Fernandez' spaces
UR - http://eudml.org/doc/215926
ER -

References

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  1. [1] N. Aronszajn and E. Gagliardo, Interpolation spaces and interpolation methods, Ann. Mat. Pura Appl. 68 (1965), 51-118. Zbl0195.13102
  2. [2] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin 1976. Zbl0344.46071
  3. [3] Yu. A. Brudnyĭ and N. Ya. Kruglyak, Interpolation Functors and Interpolation Spaces, Vol. 1, North-Holland, Amsterdam 1991. 
  4. [4] F. Cobos, T. Kühn and T. Schonbek, One-sided compactness results for Aronszajn-Gagliardo functors, J. Funct. Anal. 105 (1992), to appear. Zbl0787.46061
  5. [5] F. Cobos and J. Peetre, A multidimensional Wolff theorem, Studia Math. 94 (1989), 273-290. Zbl0716.46055
  6. [6] F. Cobos and J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. 63 (1991), 371-400. Zbl0702.46047
  7. [7] M. Cwikel and S. Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, Adv. in Math. 66 (1987), 234-290. Zbl0646.46070
  8. [8] D. L. Fernandez, Interpolation of 2 n Banach spaces, Studia Math. 45 (1979), 175-201. Zbl0462.46051
  9. [9] D. L. Fernandez, Interpolation of 2 d Banach spaces and the Calderón spaces X(E), Proc. London Math. Soc. 56 (1988), 143-162. Zbl0662.46077
  10. [10] C. Foiaş and J. L. Lions, Sur certains théorèmes d'interpolation, Acta Sci. Math. (Szeged) 22 (1961), 269-282. Zbl0127.06803
  11. [11] S. Janson, P. Nilsson, J. Peetre and M. Zafran, Notes on Wolff's note on interpolation spaces, Proc. London Math. Soc. 48 (1984), 283-299. Zbl0532.46046
  12. [12] G. Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl. 99 (1974), 247-316. Zbl0282.46022
  13. [13] T. Wolff, A note on interpolation spaces, in: Proc. Conf. on Harmonic Analysis, Minneapolis 1981, Lecture Notes in Math. 908, Springer, Berlin 1982, 199-204. 

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