Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 801531, 9 pages
http://dx.doi.org/10.1155/2014/801531
Research Article

Interpolation of Gentle Spaces

1Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Université de Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire de Recherche Équations aux Dérivées Partielles et Applications, 2092 Tunis, Tunisia

Received 1 November 2013; Revised 21 February 2014; Accepted 28 February 2014; Published 6 May 2014

Academic Editor: Paul W. Eloe

Copyright © 2014 Mourad Ben Slimane and Hnia Ben Braiek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, New York, NY, USA, 1976. View at MathSciNet
  2. R. A. Hunt, “On Lp,q spaces,” L'Enseignement Mathématique, vol. 12, pp. 249–276, 1966. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Peetre, New Thoughts on Besov Spaces, Duke University Mathematics Series I, Duke University, 1976. View at MathSciNet
  4. H. Ben Braiek, Espaces gentils et Analyse de régularité [Ph.D. thesis], Université Tunis El Manar-Université Paris, 2013.
  5. S. Jaffard, “Wavelet techniques for pointwise regularity,” Annales de la Faculté des Sciences de Toulouse. Mathématiques, vol. 15, no. 1, pp. 3–33, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Cohen, W. Dahmen, and R. deVore, “Adaptive wavelet methods for elliptic operator equations: convergence rates,” Mathematics of Computation, vol. 70, no. 233, pp. 27–75, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Jaffard, “Wavelet methods for fast resolution of elliptic problems,” SIAM Journal on Numerical Analysis, vol. 29, no. 4, pp. 965–986, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” Journal of the Royal Statistical Society B, vol. 57, no. 2, pp. 301–369, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Mallat, Wavelet Tour of Signal Processing, Academic Press, 1998. View at MathSciNet
  10. G. Bourdaud, Analyse Fonctionnelle Dans l'espace Euclidien, Publications Mathématiques de l'Université Paris VII, Paris, France, 1995. View at MathSciNet
  11. S. Rolewicz, Metric Linear Spaces, vol. 20, PWN. Warsaw, Dordrecht, Germany, 2nd edition, 1985. View at MathSciNet
  12. P. Krée, “Interpolation d'espaces vectoriels qui ne sont ni normés, ni complets. Applications,” Université de Grenoble. Annales de l'Institut Fourier, vol. 17, pp. 137–174, 1967. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. T. Holmstedt, “Interpolation of quasi-normed spaces,” Mathematica Scandinavica, vol. 26, pp. 177–199, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. Sagher, “Interpolation of r-Banach spaces,” Studia Mathematica, vol. 41, pp. 45–70, 1972. View at Google Scholar · View at MathSciNet
  15. Y. Meyer, Ondelettes et Opérateurs. I-II, Hermann, Paris, France, 1990. View at MathSciNet
  16. M. Ben Slimane and H. Ben Braiek, “On the gentle properties of anisotropic Besov spaces,” Journal of Mathematical Analysis and Applications, vol. 396, no. 1, pp. 21–48, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. Fefferman, N. M. Rivière, and Y. Sagher, “Interpolation between Hp spaces: the real method,” Transactions of the American Mathematical Society, vol. 191, pp. 75–81, 1974. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. G. Kyriazis, “Non-linear approximation and interpolation spaces,” Journal of Approximation Theory, vol. 113, no. 1, pp. 110–126, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. A. deVore and V. A. Popov, “Interpolation spaces and nonlinear approximation,” Function Spaces and Applications, vol. 1302 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. R. A. deVore, B. Jawerth, and V. Popov, “Compression of wavelet decompositions,” American Journal of Mathematics, vol. 114, no. 4, pp. 737–785, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. Cohen, R. A. deVore, and R. Hochmuth, “Restricted nonlinear approximation,” Constructive Approximation, vol. 16, no. 1, pp. 85–113, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. M. Mastyło, “On interpolation of some quasi-Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 147, no. 2, pp. 403–419, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. A.-P. Calderón and A. Torchinsky, “Parabolic maximal functions associated with a distribution. II,” Advances in Mathematics, vol. 24, no. 2, pp. 101–171, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. S. Janson and P. W. Jones, “Interpolation between Hp spaces: the complex method,” Journal of Functional Analysis, vol. 48, no. 1, pp. 58–80, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. Cwikel, M. Milman, and Y. Sagher, “Complex interpolation of some quasi-Banach spaces,” Journal of Functional Analysis, vol. 65, no. 3, pp. 339–347, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, Mass, USA, 1988. View at MathSciNet
  27. A.-P. Calderón, “Intermediate spaces and interpolation, the complex method,” Studia Mathematica, vol. 24, pp. 113–190, 1964. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. J. Peetre, “A theory of interpolation of normed spaces,” in Notas de Matematica, vol. 39, pp. 1–86, Rio de Janeiro, Brazil, 1963. View at Google Scholar
  29. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, The Netherlands, 1978. View at MathSciNet
  30. J. Peetre, “Locally analytically pseudoconvex topological vector spaces,” Studia Mathematica, vol. 63, no. 3, pp. 253–269, 1982. View at Google Scholar · View at MathSciNet
  31. F. Cobos, J. Peetre, and L. E. Persson, “On the connection between real and complex interpolation of quasi-Banach spaces,” Bulletin des Sciences Mathématiques, vol. 122, no. 1, pp. 17–37, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. P. G. Lemarié and Y. Meyer, “Ondelettes et bases hilbertiennes,” Revista Matemática Iberoamericana, vol. 2, no. 1-2, pp. 1–18, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  33. H. Triebel, Theory of Function Spaces, Monographs in Mathematics, Birkhäuser, Basel, Switzerland, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  34. R. Hanks, “Interpolation by the real method between BMO, Lα(0LTHEXAαLTHEXA) and Hα(0LTHEXAαLTHEXA),” Indiana University Mathematics Journal, vol. 26, no. 4, pp. 679–689, 1977. View at Publisher · View at Google Scholar · View at MathSciNet
  35. R. A. deVore and G. G. Lorentz, Constructive Approximation, vol. 303, Springer, Berlin, Germany, 1993. View at MathSciNet