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

• Autorzy: David Alonso-Gutiérrez , Sören Christensen , Markus Passenbrunner , Joscha Prochno
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60B99: None of the above, but in this section
• 46B45: Banach sequence spaces
• 46B07: Local theory of Banach spaces
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 3
• Strony: 269-287

Daty

wydano

2013

Twórcy

autor

David Alonso-Gutiérrez

• Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain
• Departament de Matemàtiques, Universitat Jaume I, Campus de Riu Sec, E-12071 Castelló de la Plana, Spain

autor

Sören Christensen

• Mathematisches Seminar, Christian Albrechts University Kiel, Ludewig-Meyn-Strasse 4, 24098 Kiel, Germany
• Department of Mathematics, SPST, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany

autor

Markus Passenbrunner

• Institute of Analysis, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria

autor

Joscha Prochno

• Institute of Analysis, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria

Identyfikatory

DOI

10.4064/sm219-3-6