Skip to main content

The Franklin Orthogonal System as Unconditional Basis in ReH1 and VMO

  • Chapter
Functional Analysis and Approximation

Abstract

The aim of this lecture is to present a simplified proof of P. Wojtaszczyk’s theorem that the Franklin orthogonal system is an unconditional basis in ReH1.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Billard, P., Bases dans H et bases de sous espaces de dimension finie dans A. Linear Operators and Approximation. (ISNM, vol. 20) Edited by P.L. Butzer, J.-P. Kahane and B.Sz.-Nagy. Proceedings Conf. Oberwolfach, Aug. 14–22, 1971. Birkhäuser Verlag, Basel 1972.

    Google Scholar 

  2. Bočkariov, S.V., Existence of bases in the space of analytic functions, and some properties of the Franklin system. Mat. Sbornik 95 (137), (1974), 3–18 (in Russian).

    Google Scholar 

  3. Carleson, L., An explicit unconditional basis in H 1. Institut Mittag-Leffler. Report No. 2, 1980.

    Google Scholar 

  4. Ciesielski, Z., Properties of the orthonormal Franklin system. Studia Math. 23 (1963), 141–157.

    Google Scholar 

  5. Ciesielski, Z., Properties of the orthonormal Franklin system, II. Studia Math. 27 (1966), 289–323.

    Google Scholar 

  6. Ciesielski, Z., Bases and approximation by splines. Proc. International Congress of Mathematicians. Vancouver 1974, p. 47–51.

    Google Scholar 

  7. Ciesielski, Z., Constructive function theory and spline systems. Studia Math. 53 (1975), 277–302.

    Google Scholar 

  8. Coifman, R.R. and Weiss, G., Extensions of Hardy spcaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), 569–645.

    Article  Google Scholar 

  9. Fefferman, C., Characterization of bounded mean oscillation. Bull. Amer. Math. Soc. 77 (1971), 587–588.

    Article  Google Scholar 

  10. Kwapień, S. and Pelczyński, A., Some linear topological properties of the Hardy spaces H p. Compositio Math. 33 (1976), 261–288.

    Google Scholar 

  11. Maurey, B., paper to appear in Acta Mathematica 1980.

    Google Scholar 

  12. Pełczyński, A., Banach Spaces of Analytic Functions and Absolutely Summing Operators. Conference Board of the Mathematical Sciences. Regional Conference Series in Mathematics No. 30. 1977. Amer. Math. Soc., Providence.

    Google Scholar 

  13. Riesz, M., Sur les fonctions conjuguées. Math. Z. 27 (1927), 218–244.

    Article  Google Scholar 

  14. Wojtaszczyk, P., The Franklin system is an unconditonal basis in H 1. Submitted in 1980 for Ark. Math.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Birkhäuser Verlag Basel

About this chapter

Cite this chapter

Ciesielski, Z. (1981). The Franklin Orthogonal System as Unconditional Basis in ReH1 and VMO. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-9369-5_13

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9371-8

  • Online ISBN: 978-3-0348-9369-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics