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MR1440921 (98f:60103) 60H05 (60E15 60G42)
Burkholder, Donald L. Sharp norm comparison of martingale maximal functions and stochastic integrals. Proceedings of the Norbert Wiener Centenary Congress, 1994 (East Lansing, MI, 1994), 343--358, Proc. Sympos. Appl. Math., 52, Amer. Math. Soc., Providence, RI, 1997.
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