Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-29T19:02:20.783Z Has data issue: false hasContentIssue false

Martingale inequalities

Published online by Cambridge University Press:  24 October 2008

Béla Bollobás
Affiliation:
Trinity College, Cambridge

Extract

The first result of this paper was proved in January 1975 in order to engage the interest of Professor J. E. Littlewood, who was in hospital at the time. This theorem is of some independent interest and we present it here with some related results.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Burkholder, D. L.Martingale transforms. Ann. Math. Statist. 37 (1966), 14941504.CrossRefGoogle Scholar
(2)Burkholder, D. L.Distribution function inequalities for martingales. Ann. Probability 1 (1973), 1942.CrossRefGoogle Scholar
(3)Garsia, A. M.Martingale inequalities (Benjamin, 1973).Google Scholar
(4)Hall, R. R.On a conjecture of Littlewood. Math. Proc. Cambridge Philos. Soc. 78 (1975), 443445.CrossRefGoogle Scholar
(5)Khintchine, A.Über dyadische Brüche. Math. Z. 18 (1923), 109116.CrossRefGoogle Scholar
(6)Littlewood, J. E.On bounded bilinear forms in an infinite number of variables. Quart. J. Math. Oxford 1 (1930), 164174.CrossRefGoogle Scholar
(7)Szarek, S. J.On the best constants in the Khintchine inequality. Studia Math. 18 (1976), 197208.CrossRefGoogle Scholar