Advertisement

Martingale and integral transforms of banach space valued functions

  • Jose L. Rubio de Francia
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1221)

Keywords

Banach Space Banach Lattice Singular Integral Operator Maximal Inequality Martingale Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Benedek, R. Panzone: The spaces L p with mixed norm. Duke Math. J. 28 (1961), 301–324.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    S. Bochner: Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind. Fundamenta Math. 20 (1933), 262–276.zbMATHGoogle Scholar
  3. [3]
    J. Bourgain: Some remarks on Banach spaces in which martingale differences are unconditional. Arkiv Mat. 21 (1983), 163–168.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Bourgain: Extension of a result of Benedek, Calderon and Panzone. Arkiv Mat. 22 (1984), 91–95.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J. Bourgain: Vector valued singular integrals and the H 1-BMO duality. Preprint.Google Scholar
  6. [6]
    D. L. Burkholder: Martingale Transforms. Ann. Math. Statist. 37 (1966), 1494–1504.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    D. L. Burkholder: A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Ann. Probability 9 (1981), 997–1011.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    D. L. Burkholder, R. F. Gundy: Extrapolation and interpolation of quasilinear operators on martingales. Acta. Math. 124 (1970), 249–304.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    F. Cobos: Some spaces in which martingale differences are unconditional. Preprint.Google Scholar
  10. [10]
    R. Coifman, C. Fefferman: Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51 (1974), 241–250.MathSciNetzbMATHGoogle Scholar
  11. [11]
    C. Fefferman, E. M. Stein: Some maximal inequalities. Amer. J. Math. 93 (1971), 107–115.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    J. Garcia-Cuerva, J. L. Rubio de Francia: Weighted Norm Inequalities and Related Topics. North Holland, Amsterdam, 1985.zbMATHGoogle Scholar
  13. [13]
    D. J. H. Garling: Brownian motion and UMD spaces. These Proceedings.Google Scholar
  14. [14]
    R. F. Gundy, R. L. Wheeden: Weighted integral inequalities for the nontangential maximal function, Lusin area integral and Walsh-Paley series. Studia Math. 49 (1974), 107–124.MathSciNetzbMATHGoogle Scholar
  15. [15]
    R. C. James: Super-reflexive Banach spaces. Can. J. Math. 24 (1972), 896–904.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    S. Kwapien: Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients. Studia Math. 44 (1972), 583–595.MathSciNetzbMATHGoogle Scholar
  17. [17]
    J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces II. Function Spaces. Springer-Verlag, Berlin, 1979.CrossRefzbMATHGoogle Scholar
  18. [18]
    B. Maurey: Théorèmes de Factorization pour les Opérateurs Linéaires à Valeurs dans les Espaces L p. Asterique No. 11. Soc. Math. France, 1974.Google Scholar
  19. [19]
    B. Maurey: Systeme de Haar. Sem. Maurey-Schwartz, 1974–75, Ecole Polytechnique, Paris.Google Scholar
  20. [20]
    G. Pisier: Sur les espaces de Banach qui ne contiennent pas uniformement de ℓ n1. C. R. Acad. Sci. Paris, Ser. A, 277 (1983), 991–994.MathSciNetzbMATHGoogle Scholar
  21. [21]
    G. Pisier: Martingales with values in uniformly convex spaces. Israel J. Math. 20 (1975), 326–350.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    G. Pisier: Un exemple concernant la super-reflexivite. Sem. Maurey-Schwartz, 1974, Ecole Polytechnique, Paris.Google Scholar
  23. [23]
    G. Pisier: Some applications of the complex interpolation method to Banach lattices. Journal d'Anal. Math. 35 (1979), 264–281.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    J. L. Rubio de Francia: Fourier series and Hilbert transforms with values in UMD Banach spaces. Studia Math. 81 (1985).Google Scholar
  25. [25]
    J. L. Rubio de Francia: Linear operators in Banach lattices and weighted L 2 inequalities. Math. Nachr. (1986), to appear.Google Scholar
  26. [26]
    J. L. Rubio de Francia, J. L. Torea: Some Banach techniques in vector valued Fourier Analysis. Colloquium Math., to appear.Google Scholar
  27. [27]
    J. L. Torrea: Análisis de Fourier de funciones vectoriales. Tesis, Univ. Zaragoza, 1980.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Jose L. Rubio de Francia
    • 1
  1. 1.Department of MathematicsUniversidad Autonoma de MadridMadridSpain

Personalised recommendations