Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces
Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 483-489
Voir la notice de l'article provenant de la source Math-Net.Ru
The sums of independent functions (random variables) in a symmetric space $X$ on $[0,1]$ are studied. We use the operator approach closely connected with the methods developed, primarily, by Braverman. Our main results concern the Orlicz exponential spaces $\exp(L_p)$, $1\leqslant p\leqslant\infty$, and Lorentz spaces $\Lambda_\psi$. As a corollary, we obtain results that supplement the well-known Johnson–Schechtman theorem stating that the condition $L_p\subset X$, $p\infty$, implies the equivalence of the norms of sums of independent functions and their disjoint “copies”. In addition, a statement converse, in a certain sense, to this theorem is proved.
@article{MZM_2004_76_4_a0,
author = {S. V. Astashkin and F. A. Sukochev},
title = {Comparison of {Sums} of {Independent} and {Disjoint} {Functions} in {Symmetric} {Spaces}},
journal = {Matemati\v{c}eskie zametki},
pages = {483--489},
publisher = {mathdoc},
volume = {76},
number = {4},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a0/}
}
TY - JOUR AU - S. V. Astashkin AU - F. A. Sukochev TI - Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces JO - Matematičeskie zametki PY - 2004 SP - 483 EP - 489 VL - 76 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a0/ LA - ru ID - MZM_2004_76_4_a0 ER -
S. V. Astashkin; F. A. Sukochev. Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces. Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 483-489. http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a0/