On the embedding of 2-concave Orlicz spaces into L¹

ArticleOriginal scientific text

Title

Authors ^1,²

Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078, U.S.A.
Mathematisches Seminar, Christian Albrechts Universität, 24118 Kiel, Germany

In [K-S 1] it was shown that

A v e_{π} {(\sum_{i = 1}^{n} {| x_{i} a_{π (i)} |}^{2})}^{\frac{1}{2}}

is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence

a_{1}, ..., a_{n}

so that the above expression is equivalent to a given Orlicz norm.

[B-D] J. Bretagnolle et D. Dacunha-Castelle, Application de l'étude de certaines formes linéaires aléatoires au plongement d'espaces de Banach dans les espaces $L^{p}$ , Ann. Sci. École Norm. Sup. 2 (1969), 437-480.
[K-S1] S. Kwapień and C. Schütt, Some combinatorial and probabilistic inequalities and their application to Banach space theory, Studia Math. 82 (1985), 91-106.
[K-S2] S. Kwapień and C. Schütt, Some combinatorial and probabilistic inequalities and their application to Banach space theory II, ibid. 95 (1989), 141-154.