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Note on a martingale inequality of Pisier

Published online by Cambridge University Press:  24 October 2008

David C. Cox
David C. Cox
Affiliation:
Battelle, Columbus Laboratories, Columbus, Ohio
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Extract

The principal purpose of this note is to give an elementary proof of an inequality, due to Pisier (proposition 2·4 of (4)), for martingales taking values in a Banach space X. This proof yields an explicit estimate, sharp when X is a Hilbert space, for one of the constants involved. The notation follows (1, 4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 163 - 165
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Diestel, J. Geometry of Banach Spaces -selected topics. Lecture Notes in Math. no. 485 (Springer-Verlag, New York, 1975).Google Scholar
(2)Figiel, T.On the moduli of convexity and smoothness. Studia Math. 56 (1976), 121–155.CrossRefGoogle Scholar
(3)Kemperman, J. H. B. and Smit, J. C.Sharp upper and lower bounds for the moments of a martingale. Adv. App. Prob. 6 (1974), 188.CrossRefGoogle Scholar
(4)Pisier, G.Martingales with values in uniformly convex spaces. Israel J. Math. 20 (1975), 326–350.CrossRefGoogle Scholar