Geodesic
Strong Martingale Type and Uniform Smoothness
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 159-172.

Voir la notice de l'article provenant de la source Heldermann Verlag

We introduce stronger versions of the usual notions of martingale type p ≤ 2 and cotype q ≥ 2 of a Banach space X and show that these concepts are equivalent to uniform p-smoothness and q-convexity, respectively. All these are metric concepts, so they depend on the particular norm in X. 
@article{JCA_2005_12_1_JCA_2005_12_1_a10,
     author = {J. Wenzel},
     title = {Strong {Martingale} {Type} and {Uniform} {Smoothness}},
     journal = {Journal of convex analysis},
     pages = {159--172},
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     volume = {12},
     number = {1},
     year = {2005},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a10/}
}
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J. Wenzel. Strong Martingale Type and Uniform Smoothness. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 159-172. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a10/