On the embedding of 2-concave Orlicz spaces into L¹

• Autorzy: Carsten Schütt
• Języki publikacji: EN

Abstrakty

EN

In [K-S 1] it was shown that $Ave_π(∑_{i=1}^{n} |x_i a_{π(i)}|^2)^{1/2}$ 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.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 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: 1995
• Tom: 113
• Numer: 1
• Strony: 73-80

Daty

wydano

1995

otrzymano

1994-02-22

Twórcy

autor

Carsten Schütt

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

Bibliografia

• [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.