(δ,γ)-Jacobi-Dunkl Lipschitz Functions in the Space L2(R,Aα,β(x)dx)

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R. Daher, S. El Ouadih

Abstract

Using a generalized Jacobi-Dunkl translation, we obtain an analog of Theorem 5.2 in Younis paper [7] for the Jacobi-Dunkl transform for functions satisfying the (δ,γ)-Jacobi-Dunkl Lipschitz condition in the space L2(R,Aα,β(x)dx), α ≥ β ≥-1/2, α ≠-1/2.

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References

  1. Ben Mohamed. H and Mejjaoli. H, Distributional Jacobi-Dunkl transform and applications, Afr.Diaspora J.Math 1(2004), 24-46.
  2. Ben Mohamed. H, The Jacobi-Dunkl transform on R and the convolution product on new space of distributions, Ramanujan J.21(2010), 145-175..
  3. Ben Salem. N and Ahmed Salem. A , Convolution structure associated with the Jacobi-Dunkl operator on R, Ramanuy J.12(3) (2006), 359-378.
  4. Bray. W. O and Pinsky. M. A, Growth properties of Fourier transforms via module of continuity , Journal of Functional Analysis.255(288), 2256-2285.
  5. Chouchane. F, Mili. M and Trimche. K, Positivity of the intertwining operator and harmonic analysis associated with the Jacobi-Dunkl operator on R, J.Anal. Appl.1(4)(2003), 387-412.
  6. Koornwinder. T. H, Jacobi functions and analysis on noncompact semi-simple Lie groups.in: Askey.RA, Koornwinder. T. H and Schempp.W(eds) Special Functions: Group theatrical aspects and applications.D.Reidel, Dordrecht (1984).
  7. Younis . M. S, Fourier transforms of Dini-Lipschitz functions. Int. J. Math. Math. Sci. (1986), 9 (2), 301C312. doi:10.1155/S0161171286000376
  8. Platonov. S, Approximation of functions in L2-metric on noncompact rank 1 symmetric space . Algebra Analiz .11(1) (1999), 244-270.