Advertisement

Generalized Orlicz Spaces

  • Petteri Harjulehto
  • Peter Hästö
Chapter
Part of the Lecture Notes in Mathematics book series (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.

References

  1. 20.
    V.V. Chistyakov, Metric Modular Spaces. SpringerBriefs in Mathematics (Springer, Cham, 2015). Theory and ApplicationsCrossRefGoogle Scholar
  2. 34.
    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)zbMATHGoogle Scholar
  3. 41.
    X.-L. Fan, C.-X. Guan, Uniform convexity of Musielak–Orlicz–Sobolev spaces and applications. Nonlinear Anal. 73, 163–175 (2010)MathSciNetCrossRefGoogle Scholar
  4. 50.
    P.R. Halmos, Measure Theory (D. Van Nostrand Company, New York, NY, 1950)Google Scholar
  5. 53.
    P. Harjulehto, P. Hästö, Uniform convexity and associate spaces. Czech. Math. J. 68(143)(4), 1011–1020 (2018)MathSciNetCrossRefGoogle Scholar
  6. 64.
    H. Hudzik, Uniform convexity of Orlicz–Musielak spaces with Luxemburg norm. Comment. Math. Parce Mat. 23, 21–32 (1983)zbMATHGoogle Scholar
  7. 65.
    H. Hudzik, On some equivalent conditions in Orlicz–Musielak spaces. Comment. Math. Prace Mat. 24, 57–64 (1984)MathSciNetzbMATHGoogle Scholar
  8. 71.
    M.A. Khamsi, W.M. Kozlowski, Fixed Point Theory in Modular Function Spaces (Birkhäuser/Springer, Cham, 2015). With a foreword by W. A. KirkzbMATHGoogle Scholar
  9. 74.
    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. 96.
    J. Musielak, Orlicz Spaces and Modular Spaces, volume 1034 of Lecture Notes in Mathematics (Springer, Berlin, 1983)Google Scholar
  11. 98.
    H. Nakano, Modulared Semi-Ordered Linear Spaces (Maruzen Co. Ltd., Tokyo, 1950)zbMATHGoogle Scholar
  12. 99.
    H. Nakano, Topology of Linear Topological Spaces (Maruzen Co. Ltd., Tokyo, 1951)Google Scholar
  13. 117.
    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. 122.
    W. Rudin, Functional Analysis, 2nd edn. (McGraw-Hill Book Co., New York, 1991)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Petteri Harjulehto
    • 1
  • Peter Hästö
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

Personalised recommendations