Pacific Journal of Mathematics

A Hausdorff-Young theorem for rearrangement-invariant spaces.

Colin Bennett

Article information

Source
Pacific J. Math., Volume 47, Number 2 (1973), 311-328.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102945868

Mathematical Reviews number (MathSciNet)
MR0338654

Zentralblatt MATH identifier
0262.42009

Subjects
Primary: 42A18
Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.

Citation

Bennett, Colin. A Hausdorff-Young theorem for rearrangement-invariant spaces. Pacific J. Math. 47 (1973), no. 2, 311--328. https://projecteuclid.org/euclid.pjm/1102945868


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References

  • [1] C. Bennett and J. E. Gilbert, Harmonic analysis of some function spaces on Tn, (to appear).
  • [2] D. W. Boyd, Indices of functionspaces and their relationship to interpolation, Canad. J. Math., 21 (1969), 1245-1254.
  • [3] A. P. Caldern, Spaces between L1 and L and the theorem ofMarcinkiewicz, Studia Math., 26 (1966), 273-299.
  • [4] J. E. Gilbert and C. Bennett, Interpolation Space Theory and HarmonicAnalysis, (lecture notes in preparation).
  • [5] G. H. Hardy and J. E. Littlewood, Some new properties of Fourier constants, Math. Ann., 97 (1926), 159-209.
  • [6] G. H. Hardy and J. E. Littlewood, Notes on the theory of series (XIII):Some new properties of Fourier constants, J. London Math. Soc, 6 (1931), 3-9.
  • [7] W. A. J. Luxemburg, Rearrangement-invariantBanach functionspaces, Queen's Papers in Pure and Applied Mathematics, 10 (1967), 83-144, Queen's University, Canada.
  • [8] W. A. J. Luxemburg and A. C. Zaanen, Notes on Banach function spaces, Notes I-V, Proc. Acad. Sci. Amsterdam, A 66 (Indag. 25), 135-147, 148-153, 239-250, 251-263, 496-504 (1963).
  • [9] A. Zygmund, Trigonometric Series, Vol. II, Cambridge University Press, Cambridge, 1959.