Skip to main content
SpringerLink
Log in

Dual spaces of dyadic Hardy spaces generated by a rearrangement invariant spaceX on [0,1]

  • Published:
Arkiv för Matematik

Abstract

First we define the dyadic Hardy spaceH X (d) for an arbitrary rearrangement invariant spaceX on [0, 1]. We remark that previously only a definition ofH X (d) forX with the upper Boyd indexq x <∞ was available. Then we get a natural description of the dual space ofH x , in the caseX having the property 1<-p X <-q X <2, imporoving an earlier result [P1].

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. Antipa, A., Doob's inequality for rearrangement invariant function spaces,Rev. Roumaine Math. Pures Appl. 35 (1990), 101–108.

    MATH  MathSciNet  Google Scholar 

  2. Bennett, C. andSharpley, R.,Interpolation of Operators, Academic Press, Boston, 1988.

    Google Scholar 

  3. Frazier, M. andJawerth, B., A discrete transform and decompositions of distribution spaces.J. Funct. Anal. 93 (1990), 34–170.

    Article  MathSciNet  Google Scholar 

  4. Fefferman, C. andStein, E. M., Some maximal inequalities,Amer. J. Math. 93 (1971), 107–115.

    MathSciNet  Google Scholar 

  5. Garsia, A. M.,Martingale Inequalities; Seminar Notes on Recent Progress, Benjamin, Reading-London-Amsterdam, 1973.

    Google Scholar 

  6. Johnson, W. B., Maurey, B., Schechtman, G. andTzafriri, L., Symmetric structures in Banach spaces.Mem. Amer. Math. Soc. 217 (1979).

  7. Lindenstrauss, J. andTzafriri, L.,Classical Banach Spaces I, Springer-Verlag, Berlin-Heidelberg, 1977.

    Google Scholar 

  8. Lindenstrauss, J. andTzafriri, L.,Classical Banach Spaces II, Springer-Verlag, Berlin-Heidelberg, 1979.

    Google Scholar 

  9. Popa, N., Duals of dyadic Hardy spaces generated by a rearrangement invariant function spaceX, Rev. Roumaine Math. Pures Appl. 33 (1988), 769–778.

    MATH  MathSciNet  Google Scholar 

  10. Popa, N., Isomorphism theorems for dyadic Hardy spaces generated by a rearrangement invariant spaceX on unit interval,Rev. Roumaine Math. Pures Appl. 35 (1990), 261–281.

    MATH  MathSciNet  Google Scholar 

  11. Popa, N., Dyadic Hardy spaces generated by rearrangement invariant spaces: some topological-vector space properties, inStructuri de ordine în analiza funcţionalâ (Cristescu, R., ed.), vol. 3, pp. 163–214, Editura Academiei Române, Bucharest, 1992 (Romanian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest, Romania

    Nicolae Popa

Authors
  1. Nicolae Popa
    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

Popa, N. Dual spaces of dyadic Hardy spaces generated by a rearrangement invariant spaceX on [0,1]. Ark. Mat. 36, 163–175 (1998). https://doi.org/10.1007/BF02385673

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02385673

Keywords

Search

Navigation