A notion of Orlicz spaces for vector valued functions

Gudrun Schappacher

Applications of Mathematics (2005)

  • Volume: 50, Issue: 4, page 355-386
  • ISSN: 0862-7940

Abstract

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The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on N -functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of ℒ ∞ , and representations of the dual space.

How to cite

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Schappacher, Gudrun. "A notion of Orlicz spaces for vector valued functions." Applications of Mathematics 50.4 (2005): 355-386. <http://eudml.org/doc/33227>.

@article{Schappacher2005,
abstract = {The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on $N$-functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of $\mathcal \{L\}^\{\infty \}$, and representations of the dual space.},
author = {Schappacher, Gudrun},
journal = {Applications of Mathematics},
keywords = {vector valued function; Orlicz space; Luxemburg norm; delta-growth condition; duality; vector valued function; Orlicz space; Luxemburg norm; delta-growth condition; duality},
language = {eng},
number = {4},
pages = {355-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A notion of Orlicz spaces for vector valued functions},
url = {http://eudml.org/doc/33227},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Schappacher, Gudrun
TI - A notion of Orlicz spaces for vector valued functions
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 4
SP - 355
EP - 386
AB - The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on $N$-functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of $\mathcal {L}^{\infty }$, and representations of the dual space.
LA - eng
KW - vector valued function; Orlicz space; Luxemburg norm; delta-growth condition; duality; vector valued function; Orlicz space; Luxemburg norm; delta-growth condition; duality
UR - http://eudml.org/doc/33227
ER -

References

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  9. Generalizations of Orlicz spaces of vector valued functions, PhD. Thesis, Karl Franzens University, Graz, 2003. (2003) MR2151462
  10. Interpolation of Operators. Pure and Applied Mathematics, Vol. 129, Academic Press, Boston, 1988. (1988) MR0928802
  11. Vector Measures. Hochschulbücher für Mathematik, Pergamon Press, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. (English) (1966) MR0206189

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