Skip to main content
SpringerLink
Log in

A Notion of Orlicz Spaces for Vector Valued Functions

  • Published:
Applications of Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Lemaitre, J.-L. Chaboche: Mechanics of Solid Materials. Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  2. J.-P. Aubin: Optima and Equilibria. An Introduction to Nonlinear Analysis. Springer-Verlag, Berlin, 1998.

    Google Scholar 

  3. W. Desch, R. Grimmer: On the well-posedness of constitutive laws involving dissipation potentials. Trans. Am. Math. Soc. 353 (2001), 5095–5120.

    Article  Google Scholar 

  4. M. M. Rao, Z. D. Ren: Theory of Orlicz Spaces. Pure and Applied Mathematics, Vol. 146. Marcel Dekker, New York, 1991.

    Google Scholar 

  5. M. A. Krasnosel’skij, Ya. B. Rutickij: Convex Functions and Orlicz Spaces. P. Noordhoff, Groningen, 1961.

    Google Scholar 

  6. J. Musielak: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics 1034. Springer-Verlag, Berlin, 1983.

    Google Scholar 

  7. M. S. Skaff: Vector valued Orlicz spaces. Generalized N-functions, I. Pac. J. Math. 28 (1969), 193–206.

    Google Scholar 

  8. M. S. Skaff: Vector valued Orlicz spaces, II. Pac. J. Math. 28 (1969), 413–430.

    Google Scholar 

  9. G. Schappacher: Generalizations of Orlicz spaces of vector valued functions. PhD. Thesis. Karl Franzens University, Graz, 2003.

    Google Scholar 

  10. C. Bennett, R. Sharpley: Interpolation of Operators. Pure and Applied Mathematics, Vol. 129. Academic Press, Boston, 1988.

    Google Scholar 

  11. N. Dinculeanu: Vector Measures. Hochschulbucher fur Mathematik. Pergamon Press, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. (In English.)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut fur Mathematik, Heinrichstraße 36, A-8010, Graz, Austria

    Gudrun Schappacher

Authors
  1. Gudrun Schappacher
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schappacher, G. A Notion of Orlicz Spaces for Vector Valued Functions. Appl Math 50, 355–386 (2005). https://doi.org/10.1007/s10492-005-0028-9

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10492-005-0028-9

Keywords

Search

Navigation