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Analysis Mathematica

, Volume 22, Issue 1, pp 65–79 | Cite as

MartingaleBMO spaces with continuous time

  • Ferenc Weisz
Article
  • 36 Downloads

Keywords

Continuous Time 
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.

МАРтИНгАльНыЕ пРОст РАНстВАВМО с НЕпРЕРыВНыМ ВРЕМЕН ЕМ

Abstract

ВВОДьтсь ДВА НОВых кл АссА пРОстРАНстВBMO, ИМ ЕУЩИх БОльшОЕ жНАЧЕНИЕ В тЕОРИИ ИНтЕРпОлИРО ВАНИь, И ДОкАжыВАУтсь НЕкОтОРыЕ сООтНОшЕНИь ЁкВИВАл ЕНтНОстИ Их И ОБыЧНых пРОстРАН стВBMO. ИжУЧАУтсь сООтВЕтстВУУЩИЕ “sharp”Ф УНкцИИ И ОБОБЩАУтсь НЕкОтОР ыЕ тЕОРЕМы гАРсИИ, И ФЕ ФФЕРМАНА И стЕИНА.

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References

  1. [1]
    N. L. Bassily andJ. Mogyoródi, On theBMOΦ-spaces with general Young function,Annales Univ. Sci. Budapest. Sect. Math.,27(1984), 215–227.Google Scholar
  2. [2]
    K. Bichteler, Stochastic integration andL p-theory of semimartingales.Ann. Probab.,9(1981), 49–89.MATHMathSciNetGoogle Scholar
  3. [3]
    D. L. Burkholder, Distribution function inequalities for martingales,Ann. Probab.,1(1973), 19–42.MATHMathSciNetGoogle Scholar
  4. [4]
    D. L. Burkholder andR. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales,Acta Math.,124(1970), 249–304.MathSciNetGoogle Scholar
  5. [5]
    R. R. Coifman andG. Weiss, Extensions of Hardy spaces and their use in analysis,Bull. Amer. Math. Soc.,83(1977), 569–645.MathSciNetGoogle Scholar
  6. [6]
    C. Dellacherie andP.-A. Meyer,Probabilities and potential. A, North Holland (Amsterdam, 1978).Google Scholar
  7. [7]
    C. Dellacherie andP.-A. Meyer,Probabilities and potential. B, North Holland (Amsterdam, 1982).Google Scholar
  8. [8]
    C. Fefferman andE. M. Stein,H p spaces of several variables,Acta Math.,129(1972), 137–194.MathSciNetGoogle Scholar
  9. [9]
    A. M. Garsia,Martingale inequalities, Benjamin Inc. (New York, 1973).Google Scholar
  10. [10]
    C. Herz, Bounded mean oscillation and regulated martingales,Trans. Amer. Math. Soc.,193(1974), 199–215.MATHMathSciNetGoogle Scholar
  11. [11]
    C. Herz,H p-spaces of martingales, 0<p<−1,Z. Wahrschein. Verw. Geb.,28(1974), 189–205.MATHMathSciNetGoogle Scholar
  12. [12]
    M. Metivier,Semimartingales, a course on stochastic processes, de Gruyter (Berlin-New York, 1982).Google Scholar
  13. [13]
    P.-A. Meyer, Le dual deH 1 estBMO, Seminaire de Probabilités VII, Lect. Notes Math., vol.321, pp. 136–145, Springer (Berlin-Heidelberg-New York, 1973).Google Scholar
  14. [14]
    P.-A. Meyer, Un cours les integrales stochastiques,Seminaire de Probabilités X, Lect. Notes Math., vol.511, pp. 245–400, Springer (Berlin-Heidelberg-New York, 1973).Google Scholar
  15. [15]
    J. Neveu,Discrete-parameter martingales, North Holland (Amsterdam, 1971).Google Scholar
  16. [16]
    M. Pratelli, Sur certains espaces de martingales localement de carre integrable,Seminaire de Probabilités X, Lect. Notes Math., vol.511, pp. 401–413, Springer (Berlin-Heidelberg-New York, 1976).Google Scholar
  17. [17]
    F. Weisz, Atomic Hardy spaces,Analysis Math.,20(1994), 65–80.MATHMathSciNetGoogle Scholar
  18. [18]
    F. Weisz, Interpolation between martingale Hardy andBMO spaces, the real method,Bull. Sci. Math.,116(1992), 145–158.MATHMathSciNetGoogle Scholar
  19. [19]
    F. Weisz, Interpolation between continuous parameter martingale spaces, the real method,Acta Math. Hungar.,68(1995), 37–54.CrossRefMATHMathSciNetGoogle Scholar
  20. [20]
    F. Weisz,Martingale Hardy spaces and their applications in Fourier analysis, Lecture Notes in Math., vol.1568, Springer (Berlin-Heidelberg-New York, 1994).Google Scholar
  21. [21]
    F. Weisz, Martingale Hardy spaces for 0<p<−1,Probab. Theory Related Fields,84(1990), 361–376.CrossRefMATHMathSciNetGoogle Scholar
  22. [22]
    F. Weisz, Martingale Hardy spaces with continuous time,Probability theory and applications, Essays to the memory of József Mogyoródi, Kluwer (Dordrecht-Boston-London, 1992), 47–75.Google Scholar

Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • Ferenc Weisz
    • 1
  1. 1.Department of Numerical AnalysisEötvös Loránd UniversityBudapestHungary

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