Sums of Independent Random Variables in Rearrangement Invariant Function Spaces

Johnson, William B.; Schechtman, G.

Johnson, William B. ; Schechtman, G.

Ann. Probab., Tome 17 (1989) no. 4, p. 789-808 / Harvested from Project Euclid

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Résumé

Let

$X$ be a quasinormed rearrangement invariant function space on (0, 1) which contains

$L_q(0, 1)$ for some finite

$q$ . There is an extension of

$X$ to a quasinormed rearrangement invariant function space

$Y$ on

$(0, \infty)$ so that for any sequence

$(f_i)^\infty_{i = 1}$ of symmetric random variables on (0,1), the quasinorm of

$\sum f_i$ in

$X$ is equivalent to the quasinorm of

$\sum\mathbf{f}_i$ in

$Y$ , where

$(\mathbf{f}_i)^\infty_{i = 1}$ is a sequence of disjoint functions on

$(0, \infty)$ such that for each

$i, \mathbf{f}_i$ has the same decreasing rearrangement as

$f_i$ . When specialized to the case

$X = L_q(0, 1)$ , this result gives new information on the quantitative local structure of

$L_q$ .

Publié le : 1989-04-14
Classification: Independent random variables, moment inequalities, Rosenthal's inequality, rearrangement invariant space, uniform approximation property, 60G50, 46E30

@article{1176991427,
     author = {Johnson, William B. and Schechtman, G.},
     title = {Sums of Independent Random Variables in Rearrangement Invariant Function Spaces},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 789-808},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991427}
}

Johnson, William B.; Schechtman, G. Sums of Independent Random Variables in Rearrangement Invariant Function Spaces. Ann. Probab., Tome 17 (1989) no. 4, pp.  789-808. http://gdmltest.u-ga.fr/item/1176991427/