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ArticleOriginal scientific text

Title

Hankel multipliers and transplantation operators

Authors 1, 2

Affiliations

  1. Instytut Matematyczny, Polska Akademia Nauk, Kopernika 18, 51-617 Wrocław, Poland
  2. Fachbereich Mathematik, TH Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt, Germany

Abstract

Connections between Hankel transforms of different order for Lp-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

Keywords

ENG
Hankel transform and multipliers, transplantation

Bibliography

  1. [CW] R. Coifman and G. Weiss, Some examples of transference methods in harmonic analysis, in: Symposia Math. 22, Academic Press, New York, 1977, 33-45.
  2. [EMOT] A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, Vol. 2, McGraw-Hill, New York, 1954.
  3. [GT] G. Gasper and W. Trebels, Necessary conditions for Hankel multipliers, Indiana Univ. Math. J. 31 (1982), 403-414.
  4. [Guy] D. L. Guy, Hankel multiplier transformations and weighted p-norms, Trans. Amer. Math. Soc. 95 (1960), 137-189.
  5. [He] C. Herz, On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 996-999.
  6. [Hi1] I. I. Hirschman, Jr., Multiplier transformations, II, Duke Math. J. 28 (1961), 45-56.
  7. [Hi2] I. I. Hirschman, The decomposition of Walsh and Fourier series, Mem. Amer. Math. Soc. 15 (1955).
  8. [MWY] B. Muckenhoupt, R. L. Wheeden and W.-S. Young, L2 multipliers with power weights, Adv. Math. 49 (1983), 170-216.
  9. [RdF] J. L. Rubio de Francia, Transference principles for radial multipliers, Duke Math. J. 58 (1989), 1-19.
  10. [SKM] S. G. Samko, A. A. Kilbas and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk, 1987 (in Russian).
  11. [Sch] S. Schindler, Explicit integral transform proofs of some transplantation theorems for the Hankel transform, SIAM J. Math. Anal. 4 (1973), 367-384.
  12. [To] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986.
  13. [T] W. Trebels, Some Fourier multiplier criteria and the spherical Bochner-Riesz kernel, Rev. Roumaine Math. Pures Appl. 20 (1975), 1173-1185.
  14. [W] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge, 1966.
  15. [Wi] G. M. Wing, On the Lp theory of Hankel transforms, Pacific J. Math. 1 (1951), 313-319.
  16. [Z1] A. H. Zemanian, A distributional Hankel transformation, SIAM J. Appl. Math. 14 (1966), 561-576.
  17. [Z2] A. H. Zemanian, Hankel transform of arbitrary order, Duke Math. J. 34 (1967), 761-769.
Studia Mathematica
1997/126/1
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Pages:
51-66
Main language of publication
English
Received
1996-10-07
Published
1997
Exact and natural sciences