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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FAA_2010_44_3_a12,
     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/}
}
TY  - JOUR
AU  - Yong Jiao
AU  - Tao Ma
AU  - Peide Liu
TI  - Embeddings of Lorentz Spaces of Vector-Valued Martingales
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2010
SP  - 92
EP  - 96
VL  - 44
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a12/
LA  - ru
ID  - FAA_2010_44_3_a12
ER  - 
%0 Journal Article
%A Yong Jiao
%A Tao Ma
%A Peide Liu
%T Embeddings of Lorentz Spaces of Vector-Valued Martingales
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2010
%P 92-96
%V 44
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a12/
%G ru
%F FAA_2010_44_3_a12
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/

[1] C. Bennett, R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988 | MR | Zbl

[2] J. Diestel, J. J. Uhl, Jr., Vector Measures, Amer. Math. Soc., Providence, RI, 1977 | MR | Zbl

[3] Y. Jiao, “Carleson measures and vector-valued BMO martingales”, Prob. Theo. Rel. Fields, 145:3–4 (2009), 421–434 | DOI | MR | Zbl

[4] P. D. Liu, Martingales and Geometry of Banach Spaces (in Chinese), Science Press, Beijing, 2007

[5] R-L. Long, Martingale Spaces and Inequalities, Peking University Press, Beijing, 1993 | MR | Zbl

[6] T. Martínez, J. L. Torrea, Tohoku Math. J. (2), 52 (2000), 449–474 | DOI | MR | Zbl

[7] G. Pisier, Israel J. Math., 20 (1975), 326–350 | DOI | MR | Zbl

[8] G. Peshkir, A. N. Shiryaev, UMN, 50:5 (1995), 3–62 | MR | Zbl

[9] F. Weisz, Martingale Hardy Spaces and Their Applications in Fourier Analysis, Lecture Notes in Math., 1568, Springer-Verlag, Berlin, 1994 | DOI | MR | Zbl