Science in China Series A: Mathematics

, Volume 42, Issue 1, pp 38–47 | Cite as

Atomic decompositions of Banach-spacevalued martingales

  • Peide Liu
  • Youliang Hou


Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such asH α(X) andρ H α in the case 0< α⩽ are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.


Banach-space-valued martingale martingale space atomic decomposition geometry of Banach space 


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  1. 1.
    Herz, Hρ-spaces of martingales, 0<p⩽1,Z. Wahrs. Verw. Geb., 1974,28: 189.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bernard, A., Muisonneuve, B.,Decomposition Atomique de Martingales de la Class H1 LNM, 581, Berlin: Springer-Verlag, 1977, 303–323.Google Scholar
  3. 3.
    Weisz, F.,Martingale Hardy Spaces and Their Applications in Fourier Analysis, Lecture Notes in Mathematics, Vol. 1568, Berlin: Springer-Verlag, 1994.Google Scholar
  4. 4.
    Liu, P. D., Martingale spaces and geometry of Banach spaces,Science in China, Ser. A, 1991, 34(5): 513.MATHGoogle Scholar
  5. 5.
    Liu, P. D.,Martingales and Geometry of Banach Spaces (in Chinese), Wuhan: Wuhan Univ. Press, 1993.Google Scholar
  6. 6.
    Pisier, G., Martingales in uniformly convex Banach spaces,Israel J. Math., 1975, 20: 326.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Long, R. L.,Martingale Spaces and Inequalities, Beijing: Peking Univ. Press, 1993.MATHGoogle Scholar

Copyright information

© Science in China Press 1999

Authors and Affiliations

  • Peide Liu
    • 1
  • Youliang Hou
    • 1
  1. 1.Department of MathematicsWuhan UniversityWuhanChina

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