On the Besov-Hankel spaces

Jorge J. BETANCOR; Lourdes RODRÍGUEZ-MESA

doi:10.2969/jmsj/05030781

Jorge J. BETANCOR, Lourdes RODRÍGUEZ-MESA

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Keywords: Hankel transform, L^p-spaces, Bochner-Riesz means

JOURNAL FREE ACCESS

1998 Volume 50 Issue 3 Pages 781-788

DOI https://doi.org/10.2969/jmsj/05030781

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Published: 1998 Received: October 15, 1996 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: KEYWORD Details: Right : Hankel transform, L^p-spaces, Bochner-Riesz means

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. J. Betancor and L. Rodríguez-Mesa, Lipschitz-Hankel spaces and partial Hankel integrals, to appear in Integral Transforms and Special Functions.
2) L. Colzani, A. Crespi, G. Travaglim and M. Vignati, Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in euclidean and noneuclidean spaces, Trans. Amer. Math. Soc., 338 (1) (1993), 43-55.
3) A. Erdelyi, Tables of integral transforms, II, McGraw-Hill, New York, 1953.
4) D. V. Giang and F. Móricz, A new characterization of Besov spaces on the real line, J. Math. Anal. Appl., 189 (1995), 533-551.
5) J. Gosselin and K. Stempak, A weak-type estimate for Fourier-Bessel multipliers, Proc. Amer. Math. Soc., 106 (3) (1989), 655-662.
6) D. T. Haimo, Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc., 116 (1965), 330-375.
7) C. S. Herz, On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. USA, 40 (1954), 996-999.
8) P. Heywood and P. G. Rooney, On the inversion of the even and odd Hilbert transforms, Proc. Roy. Soc. Edinburgh, 109A (1988), 201-211.
9) I. I. Hirschman, Jr., Variation diminishing Hankel transforms, J. Analyse Math., 8 (1960/61), 307-336.
10) Y. Kanjin, Convergence and divergence almost everywhere of spherical means for radial functions, Proc. Amer. Math. Soc., 103(4) (1988), 1063-1069.
11) K. Stempak, The Littlewood-Paley theory for the Fourier-Bessel transform, University of Wroclaw, Preprint n°45, 1985.
12) K. Stempak, La théorie de Littlewood-Paley pour la transformation de Fourier-Bessel, C.R. Acad. Sc. Paris, 303 (serie I, n°1) (1986), 15-19.
13) G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1959.
14) G. M. Wing, On the L^p theory of Hankel transforms, Pacific J. Math., 1 (1951), 313-319.

Right : [1] J. J. Betancor and L. Rodríguez-Mesa, Lipschitz-Hankel spaces and partial Hankel integrals, to appear in Integral Transforms and Special Functions.
[2] L. Colzani, A. Crespi, G. Travaglim and M. Vignati, Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in euclidean and noneuclidean spaces, Trans. Amer. Math. Soc., 338 (1) (1993), 43-55.
[3] A. Erdelyi, Tables of integral transforms, II, McGraw-Hill, New York, 1953.
[4] D. V. Giang and F. Móricz, A new characterization of Besov spaces on the real line, J. Math. Anal. Appl., 189 (1995), 533-551.
[5] J. Gosselin and K. Stempak, A weak-type estimate for Fourier-Bessel multipliers, Proc. Amer. Math. Soc., 106 (3) (1989), 655-662.
[6] D. T. Haimo, Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc., 116 (1965), 330-375.
[7]C. S. Herz, On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. USA, 40 (1954), 996-999.
[8] P. Heywood and P. G. Rooney, On the inversion of the even and odd Hilbert transforms, Proc. Roy. Soc. Edinburgh, 109A (1988), 201-211.
[9] I. I. Hirschman, Jr., Variation diminishing Hankel transforms, J. Analyse Math., 8 (1960/61), 307-336.
[10] Y. Kanjin, Convergence and divergence almost everywhere of spherical means for radial functions, Proc. Amer. Math. Soc., 103 (4) (1988), 1063-1069.
[11] K. Stempak, The Littlewood-Paley theory for the Fourier-Bessel transform, University of Wroclaw, Preprint n° 45, 1985.
[12] K. Stempak, La théorie de Littlewood-Paley pour la transformation de Fourier-Bessel, C. R. Acad. Sc. Paris, 303 (serie I, n° 1) (1986), 15-19.
[13] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1959.
[14] G. M. Wing, On the L^p theory of Hankel transforms, Pacific J. Math., 1 (1951), 313-319.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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