Skip to main content

Generalized Orlicz Spaces

  • Chapter
  • First Online:
Orlicz Spaces and Generalized Orlicz Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2236))

Abstract

In the previous chapter, we investigated properties of Φ-functions. In this chapter, we use them to derive results for function spaces defined by means of Φ-functions.

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

Access this chapter

eBook
USD 19.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 29.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. V.V. Chistyakov, Metric Modular Spaces. SpringerBriefs in Mathematics (Springer, Cham, 2015). Theory and Applications

    Book  Google Scholar 

  2. L. Diening, P. Harjulehto, P. Hästö, M. Růžička, Lebesgue and Sobolev spaces with Variable Exponents, volume 2017 of Lecture Notes in Mathematics (Springer, Heidelberg, 2011)

    MATH  Google Scholar 

  3. X.-L. Fan, C.-X. Guan, Uniform convexity of Musielak–Orlicz–Sobolev spaces and applications. Nonlinear Anal. 73, 163–175 (2010)

    Article  MathSciNet  Google Scholar 

  4. P.R. Halmos, Measure Theory (D. Van Nostrand Company, New York, NY, 1950)

    Google Scholar 

  5. P. Harjulehto, P. Hästö, Uniform convexity and associate spaces. Czech. Math. J. 68(143)(4), 1011–1020 (2018)

    Article  MathSciNet  Google Scholar 

  6. H. Hudzik, Uniform convexity of Orlicz–Musielak spaces with Luxemburg norm. Comment. Math. Parce Mat. 23, 21–32 (1983)

    MATH  Google Scholar 

  7. H. Hudzik, On some equivalent conditions in Orlicz–Musielak spaces. Comment. Math. Prace Mat. 24, 57–64 (1984)

    MathSciNet  MATH  Google Scholar 

  8. M.A. Khamsi, W.M. Kozlowski, Fixed Point Theory in Modular Function Spaces (Birkhäuser/Springer, Cham, 2015). With a foreword by W. A. Kirk

    MATH  Google Scholar 

  9. W.M. Kozlowski, Modular Function Spaces, volume 122 of Monographs and Textbooks in Pure and Applied Mathematics (Marcel Dekker, Inc., New York, 1988)

    Google Scholar 

  10. J. Musielak, Orlicz Spaces and Modular Spaces, volume 1034 of Lecture Notes in Mathematics (Springer, Berlin, 1983)

    Google Scholar 

  11. H. Nakano, Modulared Semi-Ordered Linear Spaces (Maruzen Co. Ltd., Tokyo, 1950)

    MATH  Google Scholar 

  12. H. Nakano, Topology of Linear Topological Spaces (Maruzen Co. Ltd., Tokyo, 1951)

    Google Scholar 

  13. M.M. Rao, Z.D. Ren, Theory of Orlicz spaces, volume 146 of Monographs and Textbooks in Pure and Applied Mathematics (Marcel Dekker Inc., New York, 1991)

    Google Scholar 

  14. W. Rudin, Functional Analysis, 2nd edn. (McGraw-Hill Book Co., New York, 1991)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Harjulehto, P., Hästö, P. (2019). Generalized Orlicz Spaces. In: Orlicz Spaces and Generalized Orlicz Spaces. Lecture Notes in Mathematics, vol 2236. Springer, Cham. https://doi.org/10.1007/978-3-030-15100-3_3

Download citation

Publish with us

Policies and ethics