Geodesic
A NECESSARY AND SUFFICIENT CONDITION FOR CERTAIN MARTINGALE INEQUALITIES IN BANACH FUNCTION SPACES
Glasgow mathematical journal, Tome 49 (2007) no. 3, pp. 431-447

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a Banach function space over a nonatomic probability space. We investigate certain martingale inequalities in X that generalize those studied by A. M. Garsia. We give necessary and sufficient conditions on X for the inequalities to be valid.
DOI : 10.1017/S0017089507003795
Mots-clés : 60G42, 46E30 
KIKUCHI, MASATO. A NECESSARY AND SUFFICIENT CONDITION FOR CERTAIN MARTINGALE INEQUALITIES IN BANACH FUNCTION SPACES. Glasgow mathematical journal, Tome 49 (2007) no. 3, pp. 431-447. doi: 10.1017/S0017089507003795
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[1] 1.Bennett, C. and Sharpley, R., Interpolation of operators, Pure and Applied Mathematics 129 (Academic Press, 1988). Google Scholar

[2] 2.Burkholder, D. L., Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. Google Scholar | DOI

[3] 3.Burkholder, D. L., Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19–42. Google Scholar | DOI

[4] 4.Chong, K. M. and Rice, N. M., Equimeasurable rearrangements of functions, Queen's Papers in Pure and Applied Mathematics, No. 28 (Queen's University, Kingston, Ontario, 1971). Google Scholar

[5] 5.Garsia, A. M., Martingale inequalities: seminar notes on recent progress (W. A. Benjamin, Inc., Massachusetts, 1973). Google Scholar

[6] 6.Kikuchi, M., Characterization of Banach function spaces that preserve the Burkholder square-function inequality, Illinois J. Math. 47 (2003), 867–882. Google Scholar | DOI

[7] 7.Kikuchi, M., New martingale inequalities in rearrangement-invariant function spaces, Proc. Edinburgh Math. Soc. (2) 47 (2004), 633–657. Google Scholar | DOI

[8] 8.Kikuchi, M., On the Davis inequality in Banach function spaces, preprint. Google Scholar

[9] 9.Kikuchi, M., On some mean oscillation inequalities for martingales, Publ. Mat., 50 (2006), 167–189. Google Scholar | DOI

[10] 10.Shimogaki, T., Hardy-Littlewood majorants in function spaces, J. Math. Soc. Japan 17 (1965), 365–373. Google Scholar

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