Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the distribution of random variables corresponding to Musielak-Orlicz norms

100%

Alonso-Gutiérrez D., Christensen S., Passenbrunner M., Prochno J.

Studia Mathematica

2013

tom 219

nr 3

269-287

Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X₁,...,Xₙ are independent copies of X, then $1/C_{p} ||x||_M ≤ 𝔼 ||(x_{i}X_{i})ⁿ_{i=1}||_{p} ≤ C_{p}||x||_M$, where $C_{p}$ is a positive constant depending only on p. In case p = 2 we need the function t ↦ tM'(t) - M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L₁[0,1]. We also provide a general result replacing the $ℓ_{p}$-norm by an arbitrary N-norm. This complements some deep results obtained by Gordon, Litvak, Schütt, and Werner [Ann. Prob. 30 (2002)]. We also prove, in the spirit of that paper, a result which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak-Orlicz spaces.

Ograniczanie wyników

1 Studia Mathematica

1 Alonso-Gutiérrez D.

1 Christensen S.

1 Passenbrunner M.

1 Prochno J.

1 2013

Wyniki wyszukiwania

On the distribution of random variables corresponding to Musielak-Orlicz norms