Burkholder, Donald L. Sharp norm comparison of martingale maximal functions and stochastic integrals. (English) Zbl 0899.60040 Mendrekar, V. (ed.) et al., Proceedings of the Norbert Wiener centenary congress, East Lansing, MI, USA, November 27–December 3, 1994. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 52, 343-358 (1997). Summary: Maximal inequalities have played an important role in analysis and probability since the work of Kolmogorov, Hardy and Littlewood, Wiener, Doob, and many others during the first half of this century. One goal here is to show how the sharp norm comparison of martingale maximal functions and stochastic integrals can be reduced to finding the upper solutions to some novel nonlinear problems. An application of the method yields the previously unknown best constant in an inequality for stochastic integrals.For the entire collection see [Zbl 0864.00070]. Cited in 1 ReviewCited in 17 Documents MSC: 60G42 Martingales with discrete parameter 60E15 Inequalities; stochastic orderings 60H05 Stochastic integrals 60G46 Martingales and classical analysis Keywords:stochastic integral; martingale; norm inequality; maximal inequality PDFBibTeX XMLCite \textit{D. L. Burkholder}, Proc. Symp. Appl. Math. 52, 343--358 (1997; Zbl 0899.60040)