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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
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(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