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Generalized Lipschitz spaces and Herz spaces on certain totally disconnected groups

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Martingale Theory in Harmonic Analysis and Banach Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 939))

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References

  1. R. E. Edwards, G. I. Gaudry, Littlewood-Paley and multiplier theory, Springer Verlag, Berlin, 1977.

    Book  MATH  Google Scholar 

  2. T. M. Flett, Some elementary inequalities for integrals with applications to Fourier transforms, Proc. London Math. Soc. (3) 29(1974), 533–556.

    MathSciNet  MATH  Google Scholar 

  3. C. Herz, Lipschitz spaces and Bernstein’s theorem on absolutely convergent Fourier transforms, J. Math. Mech. 18(1968), 283–324.

    MathSciNet  MATH  Google Scholar 

  4. E. Hewitt, K. Ross, Abstract harmonic analysis, Vol. I, II, Springer Verlag, Berlin, 1963, 1970.

    MATH  Google Scholar 

  5. R. A. Hunt, On (L(p,q) spaces, l’Enseignement Math. 12(1966), 249–276.

    Google Scholar 

  6. R. Johnson, Lipschitz spaces, Littlewood-Paley spaces, and convoluteurs, Proc. London Math. Soc. (3) 28(1974), 127–141.

    Article  MathSciNet  MATH  Google Scholar 

  7. C. N. Kellogg, An extension of the Hausdorff-Young theorem, Mich. Math. J. 18(1971), 121–128.

    Article  MathSciNet  MATH  Google Scholar 

  8. I. Mozejko, On absolute convergence of Fourier series, Functiones et Approximatio Comm. Math. 2(1976), 177–182.

    MathSciNet  MATH  Google Scholar 

  9. C. J. Neugebauer, The LP modulus of continuity and Fourier series of Lipschitz functions, Proc. Amer. Math. Soc. 64(1977), 71–76.

    MathSciNet  MATH  Google Scholar 

  10. H. Ombe, personal communication.

    Google Scholar 

  11. C. W. Onneweer, Absolute convergence of Fourier series on certain groups, Duke. Math. J. 39(1972), 599–609.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Peetre, Applications de la théorie des espaces d’interpolation dans l’analyse harmonique, Ricerche Mat.15(1966), 1–37.

    MathSciNet  MATH  Google Scholar 

  13. T. S. Quek, L. Y. H. Yap, Absolute convergence of Vilenkin-Fourier series, J. Math. Anal. Appl. 74(1980), 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  14. N. M. Rivière, Y. Sagher, On two theorems of Paley, Proc. Amer. Math. Soc. 42(1974), 238–242.

    Article  MathSciNet  MATH  Google Scholar 

  15. R. Spector, Sur la structure locale des groupes abéliens localement compacts, Bull. Soc. Math. France, Mémoire 24, 1970.

    Google Scholar 

  16. M. H. Taibleson, Fourier analysis on local fields, Math. Notes Princeton Univ. Press, Princeton, 1975.

    MATH  Google Scholar 

  17. H. Triebel, Interpolation theory, function spaces. differential operators, VEB Deutscher Verlag Wissenschaften, Berlin, 1978.

    MATH  Google Scholar 

  18. H. Triebel, Spaces of Besov-Hardy-Sobolev Type, Teubner Texte Math., Teubner, Leipzig, 1978.

    Google Scholar 

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Jia-Arng Chao Wojbor A. Woyczyński

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© 1982 Springer-Verlag

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Onneweer, C.W. (1982). Generalized Lipschitz spaces and Herz spaces on certain totally disconnected groups. In: Chao, JA., Woyczyński, W.A. (eds) Martingale Theory in Harmonic Analysis and Banach Spaces. Lecture Notes in Mathematics, vol 939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096263

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  • DOI: https://doi.org/10.1007/BFb0096263

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  • Print ISBN: 978-3-540-11569-4

  • Online ISBN: 978-3-540-39284-2

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