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Banach Spaces, Harmonic Analysis, and Probability Theory pp 123–154Cite as

Some applications of the metric entropy condition to harmonic analysis

Part of the Lecture Notes in Mathematics book series (LNM,volume 995)

Keywords

  • Banach Space
  • Gaussian Process
  • Sample Path
  • Banach Lattice
  • Orlicz Space

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References

  1. C. Bennett. Intermediate spaces and the class L log+ L. Arkiv för Matematik 11 (1973) 215–228.

    MathSciNet  CrossRef  MATH  Google Scholar 

  2. J. Bergh, J. Löfström. Interpolation spaces. Springer Verlag, Berlin, Heidelberg, New York (1976).

    CrossRef  MATH  Google Scholar 

  3. R. M. Dudley. The size of compact subsets of Hilbert space and continuity of Gaussian processes. Journal of Funct. Analysis 1 (1967) 290–330.

    MathSciNet  CrossRef  MATH  Google Scholar 

  4. X. Fernique. Régularité des trajectoires des processus gaussiens. Ecole d’Ete de ST Flour. Springer Lecture Notes no480.

    Google Scholar 

  5. A. Garsia. A remarkable inequality and the uniform convergence of Fourier series. Indiana Univ. Math Journal 25 (1976) 85–102.

    MathSciNet  CrossRef  MATH  Google Scholar 

  6. N. Kôno. Sample paths properties of stochastic processes. J. Math Kyoto Univ. 20 (1980) 295–313.

    MathSciNet  MATH  Google Scholar 

  7. M. B. Marcus and G. Pisier. Random Fourier series with Applications to Harmonic Analysis. Annals of Math Studies. no101 (1981) Princeton University Press.

    Google Scholar 

  8. G. Pisier. Sur l’espace des series de Fourier aléatoires presque sûrement continues. Exposé no 17–18, Seminaire sur la géométrie des espaces de Banach. Ecole Polytechnique, Palaiseau, 1977/78.

    Google Scholar 

  9. G. Pisier. A remarkable homogeneous Banach algebra. Israel J. Math 34 (1979) 38–44.

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. G. Pisier. Conditions d’entropie assurant la continuité de certains processus et applications a l’analyse harmonique. Seminaire d’analyse fonctionnelle. Expose no13–14. Ecole Polytechnique, Palaiseau, 1979/80.

    Google Scholar 

  11. G. Pisier. De nouvelles caractérisations des ensembles de Sidon. Advances in Maths. Supplementary Studies. (1981) Vol. 7B, p. 685.

    MathSciNet  MATH  Google Scholar 

  12. J. H. Wells, L. R. Williams. Embeddings and extensions in analysis, Springer Verlag (1975), Ergebnisse Band 84.

    Google Scholar 

  13. M. Zafran. The dichotomy problem for homogeneous Banach algebras. Annals of Maths. 108 (1978) 97–105.

    MathSciNet  CrossRef  MATH  Google Scholar 

  14. M. B. Marcus and G. Pisier. Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes. To appear.

    Google Scholar 

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Authors
  1. Gilles Pisier
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    © 1983 Springer-Verlag

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    Pisier, G. (1983). Some applications of the metric entropy condition to harmonic analysis. In: Blei, R.C., Sidney, S.J. (eds) Banach Spaces, Harmonic Analysis, and Probability Theory. Lecture Notes in Mathematics, vol 995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061891

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    • DOI: https://doi.org/10.1007/BFb0061891

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-12314-9

    • Online ISBN: 978-3-540-40036-3

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