Geodesic
Embeddings of Lorentz Spaces of Vector-Valued Martingales
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 92-96

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We obtain new embedding theorems for Lorentz spaces of vector-valued martingales, thus generalizing the classical martingale inequalities. In contrast to earlier methods, we use martingale transformations defined by sequences of operators and identify the operator $S^{(p)}(f)$ for a martingale $f$ ranging in a Banach space $X$ with the maximal operator for some $\ell^p(X)$-valued martingale transform. The obtained inequalities are closely related to geometric properties of the Banach space in question.
Keywords: martingale Lorentz space, embedding, uniformly convex space, uniformly smooth space. 
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     author = {Yong Jiao and Tao Ma and Peide Liu},
     title = {Embeddings of {Lorentz} {Spaces} of {Vector-Valued} {Martingales}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {92--96},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a12/}
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Yong Jiao; Tao Ma; Peide Liu. Embeddings of Lorentz Spaces of Vector-Valued Martingales. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 92-96. http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a12/