Symmetric Besov-Bessel Spaces

Houissa, Khadija; Sifi, Mohamed

doi:10.2478/auom-2014-0051

Abstract

In this paper we introduce the symmetric Besov-Bessel spaces. Next, we give a Sonine formula for generalized Bessel functions. Finally, we give a characterization of these spaces using the Bochner-Riesz means.

References

[1] J.J. Betancor and L. Rodriguez-Mesa, On the Besov-Hankel spaces, J.Math. Soc. Japan, 50, n:3 (1998), 781-788.10.2969/jmsj/05030781
Search in Google Scholar
[2] J.J. Betancor and L. Rodriguez-Mesa, Lipschitz-Hankel spaces and partial Hankel integrals, Integral trnsforms. Spec.Funct.7, n:1-2 (1998), 1-12.10.1080/10652469808819181
Search in Google Scholar
[3] J.J. Betancor and L. Rodriguez-Mesa, Lipschitz-Hankel spaces, partial Hankel integrals and Bochner-Riesz means, Arch. Math. 71, :2 (1998), 115-122.10.1007/s000130050242
Search in Google Scholar
[4] J. Faraut and A. Koranyi, Analysis on symmetric cones, Oxford Science Publications, Clarendon press, Oxford 1994.
Search in Google Scholar
[5] J. Faraut and G. Travaglini, Bessel functions associated with representations of formally real Joradn algebras, J. Funct. Anal. 71 (1987), 123-141.10.1016/0022-1236(87)90019-X
Search in Google Scholar
[6] D.V. Giang and F. Moricz, A new characterization of Besov spaces on the real line, J. Math. Anal. Appli. 189 (1995), 533-551.10.1006/jmaa.1995.1034
Search in Google Scholar
[7] K. Gross, D. Richards, Special functions of matrix argument I: Algebric induction, zonal polynomials, and hypergeometric functions, Trans. Amer. Math. Sos. 301 (1987), 781-811.
Search in Google Scholar
[8] C.S. Herz, Bessel functions of matrix argument, Ann. Math. 61 (1955), 474-523.10.2307/1969810
Search in Google Scholar
[9] K. Houissa and M. Sifi, Symmetric Bessel multipliers, Colloq. Math. Vol. 126, no. 2, (2012), 155-176.10.4064/cm126-2-2
Search in Google Scholar
[10] M. de Jeu and M. Rösler, Asymptotic analysis for the Dunkl kernel, J. Approx. Theory 119 (2002), 110–126.10.1006/jath.2002.3722
Search in Google Scholar
[11] R.I. Jewett, Spaces with an anstract convolution of measures, Adv. Math. 18 (1975), 1-101.10.1016/0001-8708(75)90002-X
Search in Google Scholar
[12] J. Kaneko, Selberg integrals and hypergeometric functions associated with Jack polynomials, SIAM J. Math. Anal. 24 (993), 1086-1100.10.1137/0524064
Search in Google Scholar
[13] L. Kamoun, Besov-type spaces for the Dunkl operator on the real line, J. Comput. Appl. Math. 199 (2007), no. 1, 5667.
Search in Google Scholar
[14] E.M. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group, Composito Math. 85 (1993), 333-373.
Search in Google Scholar
[15] M. Rösler, Bessel convolutions on matrix cones, Composito Math. 143 (2007), 749-779.10.1112/S0010437X06002594
Search in Google Scholar
[16] E.M. Stein and G. Weiss, Introduction to Fourier Analysis on euclidean spaces, Princeton Univ. Press, New Jersey, 1971.10.1515/9781400883899
Search in Google Scholar

Symmetric Besov-Bessel Spaces

Abstract

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