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Acta Mathematica Hungarica

, Volume 148, Issue 2, pp 360–369 | Cite as

On a Theorem of F. Riesz

  • H. H. BangEmail author
Article
  • 86 Downloads

Abstract

We prove a theorem of Riesz characterizing the convergence in spaces of functions N ɸ generated by concave functions ɸ.

Keywords and phrases

measure Orlicz space Lorentz space 

Mathematics Subject Classification

46F99 46E30 

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References

  1. 1.
    Bang H. H., Cong N. M.: Generalizations of the Riesz convergence theorem for Lorentz spaces, Acta Math. Hungar., 106, 331–341 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    P. R. Halmos, Measure Theory, Springer-Verlag, (New York, 1974).Google Scholar
  3. 3.
    Lorentz G. G.: Some new function spaces, Ann. Math., 51, 37–55 (1950)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lorentz G. G.: Relations between function spaces, Proc. Amer. Math. Soc., 12, 127–132 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    O’Neil R.: Convolution operators and L(p, q) spaces, Duke Math. J., 30, 120–142 (1963)MathSciNetzbMATHGoogle Scholar
  6. 6.
    M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker Inc., (New York, 1995).Google Scholar
  7. 7.
    F. Riesz, Sur la convergence en moyenne, Acta Sci. Math. (Szeged), 4 (1928), 58-64 and 182-185.Google Scholar
  8. 8.
    Sargent W. L. C.: Some sequence spaces related to the l p spaces, J. London Math. Soc., 35, 161–171 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Sargent W. L. C.: Some analogues and extensions of Marcinkiewicz’s interpolation theorem, Proc. London Math. Soc., 11, 457–468 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Steigerwalt M. S., White A. J.: Some function spaces related to L p, Proc. London. Math. Soc., 22, 137–163 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    M. S. Steigerwalt, Some Banach Function Spaces Related to Orlicz Spaces, Thesis, University of Aberdeen (1967).Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.Institute of MathematicsVietnamese Academy of Science and TechnologyCau Giay, HanoiVietnam

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