Analysis Mathematica

, Volume 23, Issue 1, pp 45–75 | Cite as

Inequalities and duality results with respect to two-parameter strong martingales

  • Ferenc Weisz
  • Ф. ВЕИС
Article
  • 44 Downloads

Keywords

Hardy Space Quadratic Variation Atomic Decomposition Duality Result Strong Atom 
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.

Неравенства и соотнощения двоиственности для многопараметричес ких силяных мартингалов

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References

  1. [1]
    A. Bernard, EspacesH 1 de martingales à deux indices. Dualité avec les martingales de typeBMO, Bull. Sci. Math.,103(1979), 297–303.MATHMathSciNetGoogle Scholar
  2. [2]
    J. Brossard, Comparaison des “normes”L p du processus croissant et de la variable maximale pour les martingales régulières à deux indices. Théorème local correspondant,Annals of Probab.,8(1980), 1183–1188.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    J. Brossard,Régularités des martingales à deux indices et inégalités de normes, Processus aléatoires à deux indices, Lect. Notes Math., Vol.863, 91–121, Springer (Berlin-Heidelberg-New York, 1981).CrossRefGoogle Scholar
  4. [4]
    D. L. Burkholder, Distribution function inequalities for martingales,Annals of Probab.,1(1973), 19–42.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    D. L. Burkholder, B. J. Davis andR. F. Gundy, Integral inequalities for convex functions of operators on martingales,Proc. Sixth Berkeley Symp. Math. Stat. and Probab., 223–240, Univ. California Press (Berkeley, California, 1972).Google Scholar
  6. [6]
    D. L. Burkholder andR. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales,Acta Math.,124(1970), 249–304.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    R. Cairoli, Une inégalité pour martingale à indices multiples et ses applications,Séminaire de Probabilités IV, Lect. Notes Math., vol.124, pp. 1–27, Springer (Berlin-Heidelberg-New York, 1970).Google Scholar
  8. [8]
    R. Cairoli andJ. B. Walsh, Stochastic integrals in the plane,Acta Math.,134(1975), 111–183.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    B. J. Davis, On the integrability of the martingale square function,Israel J. Math.,8(1970), 187–190.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    N. E. Frangos andP. Imkeller, Some inequalities for strong martingales,Ann. Inst. Henri Poincaré,24(1988), 395–402.MATHMathSciNetGoogle Scholar
  11. [11]
    A. M. Garsia,Martingale inequalities, Seminar Notes on Recent Progress, Math. Lecture Notes, Benjamin Inc. (New York, 1973).MATHGoogle Scholar
  12. [12]
    R. F. Gundy,Inégalités pour martingales à un et deux indices: L’espace H p, Ecole d’Eté de Probabilités de Saint-Flour VIII-1978, Lect. Notes Math., vol.774, 251–331, Springer (Berlin-Heidelberg-New York, 1980).CrossRefGoogle Scholar
  13. [13]
    C. Herz, Bounded mean oscillation and regulated martingales,Trans. Amer. Math. Soc.,193(1974), 199–215.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    C. Herz,H p-spaces of martingales, 0<p ≤ 1,Z. Wahrsch. verw. Gebiete,28(1974), 189–205.MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    P. Imkeller, A stochastic calculus for continuousN-parameter strong martingales,Stochastic Process. App.,20(1985), 1–40.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    P. Imkeller,Two-parameter martingales and their quadratic variation, Lect. Notes Math., vol.1308, Springer (Berlin-Heidelberg-New York, 1988).MATHGoogle Scholar
  17. [17]
    M. Ledoux, ClasseL logL et martingales fortes à paramètre bidimensionnel,Ann. Inst. H. Poincaré, Sect. B,17(1981), 275–280.MATHMathSciNetGoogle Scholar
  18. [18]
    M. Ledoux, Transformées de Burkholder et sommabilité de martingales à deux paramètres,Math. Z.,181(1982), 529–535.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    E. Merzbach, Stopping for two-dimensional stochastic processes,Stochastic Process. Appl.,10(1980), 49–63.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    C. Metraux, Quelques inégalités pour martingales à parametre bidimensional,Séminaire de Probabilités XII, Lect. Notes Math., vol.649, 170–179, Springer (Berlin-Heidelberg-New York, 1978).CrossRefGoogle Scholar
  21. [21]
    J. Neveu,Discrete-parameter martingales, North Holland (Amsterdam, 1971).Google Scholar
  22. [22]
    M. Pratelli, Sur certains espaces de martingales localement de carré intégrable,Séminaire de Probabilités X, Lect. Notes Math., vol.511, 401–413, Springer (Berlin-Heidelberg-New York, 1976).Google Scholar
  23. [23]
    F. Schipp, W. R. Wade, P. Simon andJ. Pál,Walsh series: An introduction to dyadic harmonic analysis, Adam Hilger (Bristol-New York, 1990).MATHGoogle Scholar
  24. [24]
    E. M. Stein,Topics in harmonic analysis, University Press (Princeton, 1970).MATHGoogle Scholar
  25. [25]
    J. B. Walsh, Convergence and regularity of multiparameter strong martingales,Z. Wahrsch. verw. Gebiete,46(1974), 177–192.CrossRefGoogle Scholar
  26. [26]
    F. Weisz, An application of two-parameter martingales in harmonic analysis,Studia Math.,107(1993), 115–126.MATHMathSciNetGoogle Scholar
  27. [27]
    F. Weisz, Interpolation between two-parameter martingale Hardy spaces, the real method,Bull. Sci. Math.,115(1991), 253–264.MATHMathSciNetGoogle Scholar
  28. [28]
    F. Weisz, Martingale Hardy spaces for 0<p ≤ 1,Probab. Theory Related Fields,84(1990), 361–376.MATHCrossRefMathSciNetGoogle Scholar
  29. [29]
    F. Weisz, On duality problems of two-parameter martingale Hardy spaces,Bull. Sci. Math.,114(1990), 395–410.MATHMathSciNetGoogle Scholar
  30. [30]
    F. Weisz, One-parameter martingale inequalities,Annales Univ. Sci. Budapest. Sect. Comput.,14(1994), 249–278.MATHMathSciNetGoogle Scholar
  31. [31]
    E. Wong andM. Zakai, Weak martingales and stochastic integrals in the plane,Annals of Probab.,4(1976), 570–586.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 1997

Authors and Affiliations

  • Ferenc Weisz
    • 1
  • Ф. ВЕИС
    • 1
  1. 1.Department of Numerical AnalysisL. Eötvös UniversityBudapestHungary

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