Random Martingale Transform Inequalities

  • D. J. H. Garling
Part of the Progress in Probability book series (PRPR, volume 20)


Certain inequalities play a fundamental role in the theory of martingales. In order to describe these, let us begin by describing the notation that we use. Because we wish to transform martingales in a random way, the setting is a little more complicated than usual.


Banach Space Haar Measure Banach Lattice Unconditional Basis Predictable Process 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D.J. Aldous, Unconditional bases and martingales in LP(F), Math. Proc. Cambridge Phil. Soc. 85 (1979), 117–123.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    J. Bourgain, Some remarks on Bonach spaces in which martingale difference sequences are unconditional, Arkiv Math. 21 (1983), 163–168.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    D.L. Burkholder, A geometric characterization of Banach spaces in which martingale difference sequences are unconditional, Annals of Probability 9 (1981), 997–1011.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    D.L. Burkholder,, A geometric condition that implies the existence of cer- tain singular integrals of Banach-space valued functions, Proceedings of a conference on Harmonic Analysis, Volume 1. ( Belmont, Wadsworth International, 1983 ).Google Scholar
  5. [5]
    D.L. Burkholder, Boundary value problems and sharp inequalities for mar- tingale transforms, Annals of Probability 12 (1984), 647–702.MathSciNetMATHCrossRefGoogle Scholar
  6. ], An elementary proof of an inequality of R.E.A.C. Paley, Bull. London Math. Soc. 17 (1985), 474–478.CrossRefGoogle Scholar
  7. [7]
    J.L. Doob, Stochastic Processes. Wiley, New York, 1953.MATHGoogle Scholar
  8. [8]
    A. Garsia, Martingale inequalities: seminar notes on recent progress. ( Reading, Benjamin, 1973 ).MATHGoogle Scholar
  9. [9]
    J.-P. Kahane, Some random series of functions. ( 2nd Edn., Cambridge, C.U.P., 1985 ).MATHGoogle Scholar
  10. [10]
    J.- Lindenstrauss and L. Tzafriri, Classical Banach space II. Springer-Verlag, Berlin, 1979.Google Scholar
  11. [11]
    B. Maurey and G. Pisier, Series de variables aleatoires vectorielles independantes et proprietes geometriques des espaces de Banach, Studia Math. 58 (1976), 45–90.MathSciNetMATHGoogle Scholar
  12. [12]
    G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326–350.MathSciNetMATHGoogle Scholar

Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • D. J. H. Garling

There are no affiliations available

Personalised recommendations