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)


Banach Space Banach Lattice Singular Integral Operator Maximal Inequality Martingale Difference 
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  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

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