Skip to main content
SpringerLink
Log in

Multipliers of Lp and the operational calculus

  • Conference paper
  • First Online:
Harmonic Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 908))

  • 643 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
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. W. J. Bailey, G. Brown, and W. Moran, “Spectra of independent power measures,” Proc. Camb. Philos. Soc., 72 (1972), 27–35.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Brown, and W. Moran, “A dichotomy for infinite convolutions of discrete measures,” Proc. Camb. Philos. Soc., 73 (1973), 307–316.

    Article  MathSciNet  MATH  Google Scholar 

  3. N. Dunford, and J. Schwartz, Linear Operators, part II, Interscience Publishers, New York, 1963.

    MATH  Google Scholar 

  4. A. Figà-Talamanca, and G. Gaudry, “Multipliers of LP which vanish at infinity,” J. Functional Analysis, 7 (1971), 475–486.

    Article  MathSciNet  MATH  Google Scholar 

  5. C. Graham, and O. C. McGehee, Essays in Commutative Harmonic Analysis, Pringer-Verlag, New York, 1979.

    Book  MATH  Google Scholar 

  6. H. Helson, and J.-P. Kahane, “Sur les fonctions opérant dans les algèbres de transformées de Fourier de suites ou de fonctions sommables,” C. R. Acad. Sci. Paris, Sér. A-B, 247 (1958), A626–A628.

    MathSciNet  MATH  Google Scholar 

  7. H. Helson, J.-P. Kahane, Y. Katznelson, and W. Rudin, “The functions which operate on Fourier transforms,” Acta Math., 102 (1959), 135–157.

    Article  MathSciNet  MATH  Google Scholar 

  8. L. Hörmander, “Estimates for translation invariant operators in Lp spaces,” Acta Math., 104 (1960), 93–140.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Igari, “Functions of Lp multipliers,” Tôhoku Math. J., 21 (1969), 304–320.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Igari, “Functions of Lp multipliers II,” Tôhoku Math. J., 26 (1974), 555–561.

    Article  MathSciNet  MATH  Google Scholar 

  11. J.-P. Kahane, Séries de Fourier Absolument Convergentes, Springer-Verlag, New York, 1970.

    MATH  Google Scholar 

  12. J.-P. Kahane, and W. Rudin, “Charactérisation des fonctions qui opèrent sur les coefficients de Fourier-Stieltjes,” C. R. Acad. Sci. Paris, Sér. A-B, 247 (1958), 773–775.

    MathSciNet  MATH  Google Scholar 

  13. J.-P. Kahane, and R. Salem, Ensembles Parfaits et Séries Trigonométriques,” Hermann, Paris, 1963.

    MATH  Google Scholar 

  14. Y. Katznelson, An Introduction to Harmonic Analysis, Dover, New York, 2nd edition, 1976.

    MATH  Google Scholar 

  15. Y. Katznelson, “Sur les fonctions opérant sur l’algèbre des séries de Fourier absolument convergentes,” C. R. Acad. Sci. Paris, Sér. A-B, 247 (1958), 404–406.

    MathSciNet  MATH  Google Scholar 

  16. Y. Katznelson, “Sur le calcul symbolique dans quelques algèbres de Banach,” Ann. Sci. Ecole Norm. Sup., 76 (1959), 83–123.

    MathSciNet  MATH  Google Scholar 

  17. P. Lévy, “Sur la convergence absolue des séries de Fourier,” Compositio Math., 1 (1934), 1–14.

    MATH  Google Scholar 

  18. L. Loomis, An Introduction to Abstract Harmonic Analysis, Van Nostrand, New York, 1953.

    MATH  Google Scholar 

  19. W. Rudin, Fourier Analysis on Groups, Interscience Publishers, New York, 2nd printing, 1967.

    MATH  Google Scholar 

  20. W. Rudin, “Fourier-Stieltjes transforms of measures on independent sets,” Bull. Amer. Math. Soc., 66 (1960), 199–202.

    Article  MathSciNet  MATH  Google Scholar 

  21. W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973.

    MATH  Google Scholar 

  22. W. Rudin, “A strong converse of the Wiener-Lévy theorem,” Canad. J. Math., 14 (1962), 694–701.

    Article  MathSciNet  MATH  Google Scholar 

  23. Yu. Šreider, “The structure of maximal ideals in rings of measures with convolution,” Mat. U.S.S.R. Sb., 27 (1950), 297–318; Amer. Math. Soc. Translation 81 (1953).

    MathSciNet  Google Scholar 

  24. J. L. Taylor, “Measure algebras,” Regional conference series in Mathematics, no. 16, Amer. Math. Soc., Providence, R. I., 1973.

    Book  MATH  Google Scholar 

  25. N. Varopoulos, “Sur les mesures de Radon d’un groupe localement compact abelian,” C. R. Acad. Sci. Paris, Sér. A-B, 258 (1964), 3805–08 and 4896–99; 260 (1965), 1059–62.

    MATH  Google Scholar 

  26. N. Varopoulos, “The functions that operate on Bo(Γ) of a discrete group Γ,” Bull. Soc. Math. France, 93 (1965), 301–321.

    MathSciNet  Google Scholar 

  27. N. Wiener, “Tauberian theorems,” Ann. of Math., 33 (1932), 1–100.

    Article  MathSciNet  MATH  Google Scholar 

  28. N. Wiener, and R. Pitt, “On absolutely convergent Fourier-Stieltjes transforms,” Duke Math. J., 4 (1938), 420–436.

    Article  MathSciNet  MATH  Google Scholar 

  29. J. H. Williamson, “A theorem on algebras of measures on topological groups,” Proc. Edinburgh Philos. Soc., 11 (1959), 195–206.

    Article  MathSciNet  MATH  Google Scholar 

  30. M. Zafran, “Exponential estimates in multiplier algebras”, submitted for publication.

    Google Scholar 

  31. M. Zafran, “On the spectra of multipliers,” Pacific J. Math., 47 (1973). 609–626.

    Article  MathSciNet  MATH  Google Scholar 

  32. M. Zafran, “The spectra of multiplier transformations on the Lp spaces,” Ann. of Math., 103 (1976), 355–374.

    Article  MathSciNet  MATH  Google Scholar 

  33. M. Zafran, “The functions operating on multiplier algebras,” J. Functional Analysis, 26 (1977), 289–314.

    Article  MathSciNet  MATH  Google Scholar 

  34. A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, Cambridge, England, 1968, vol. I and II.

    MATH  Google Scholar 

Download references

Authors
  1. Misha Zafran
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Fulvio Ricci Guido Weiss

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Zafran, M. (1982). Multipliers of Lp and the operational calculus. In: Ricci, F., Weiss, G. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093292

Download citation

  • DOI: https://doi.org/10.1007/BFb0093292

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11188-7

  • Online ISBN: 978-3-540-38973-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation