# Hankel multipliers and transplantation operators

Krzysztof Stempak; Walter Trebels

Studia Mathematica (1997)

- Volume: 126, Issue: 1, page 51-66
- ISSN: 0039-3223

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topStempak, Krzysztof, and Trebels, Walter. "Hankel multipliers and transplantation operators." Studia Mathematica 126.1 (1997): 51-66. <http://eudml.org/doc/216443>.

@article{Stempak1997,

abstract = {Connections between Hankel transforms of different order for $L^p$-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.},

author = {Stempak, Krzysztof, Trebels, Walter},

journal = {Studia Mathematica},

keywords = {Hankel transform and multipliers; transplantation; Hankel transforms; Bessel functions; radial Fourier multipliers; Hankel multipliers},

language = {eng},

number = {1},

pages = {51-66},

title = {Hankel multipliers and transplantation operators},

url = {http://eudml.org/doc/216443},

volume = {126},

year = {1997},

}

TY - JOUR

AU - Stempak, Krzysztof

AU - Trebels, Walter

TI - Hankel multipliers and transplantation operators

JO - Studia Mathematica

PY - 1997

VL - 126

IS - 1

SP - 51

EP - 66

AB - Connections between Hankel transforms of different order for $L^p$-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.

LA - eng

KW - Hankel transform and multipliers; transplantation; Hankel transforms; Bessel functions; radial Fourier multipliers; Hankel multipliers

UR - http://eudml.org/doc/216443

ER -

## References

top- [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.
- [EMOT] A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, Vol. 2, McGraw-Hill, New York, 1954. Zbl0055.36401
- [GT] G. Gasper and W. Trebels, Necessary conditions for Hankel multipliers, Indiana Univ. Math. J. 31 (1982), 403-414. Zbl0494.44003
- [Guy] D. L. Guy, Hankel multiplier transformations and weighted p-norms, Trans. Amer. Math. Soc. 95 (1960), 137-189. Zbl0091.10202
- [He] C. Herz, On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 996-999. Zbl0059.09901
- [Hi1] I. I. Hirschman, Jr., Multiplier transformations, II, Duke Math. J. 28 (1961), 45-56.
- [Hi2] I. I. Hirschman, The decomposition of Walsh and Fourier series, Mem. Amer. Math. Soc. 15 (1955).
- [MWY] B. Muckenhoupt, R. L. Wheeden and W.-S. Young, ${L}^{2}$ multipliers with power weights, Adv. Math. 49 (1983), 170-216.
- [RdF] J. L. Rubio de Francia, Transference principles for radial multipliers, Duke Math. J. 58 (1989), 1-19.
- [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). Zbl0617.26004
- [Sch] S. Schindler, Explicit integral transform proofs of some transplantation theorems for the Hankel transform, SIAM J. Math. Anal. 4 (1973), 367-384. Zbl0227.44007
- [To] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986.
- [T] W. Trebels, Some Fourier multiplier criteria and the spherical Bochner-Riesz kernel, Rev. Roumaine Math. Pures Appl. 20 (1975), 1173-1185. Zbl0328.42003
- [W] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, Cambridge, 1966. Zbl0174.36202
- [Wi] G. M. Wing, On the ${L}^{p}$ theory of Hankel transforms, Pacific J. Math. 1 (1951), 313-319. Zbl0044.10906
- [Z1] A. H. Zemanian, A distributional Hankel transformation, SIAM J. Appl. Math. 14 (1966), 561-576. Zbl0154.13803
- [Z2] A. H. Zemanian, Hankel transform of arbitrary order, Duke Math. J. 34 (1967), 761-769. Zbl0177.39903

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