Title: (δ,γ)-Jacobi-Dunkl Lipschitz Functions in the Space L2(R,Aα,β(x)dx)
Author(s): R. Daher, S. El Ouadih
Pages: 123-129
Cite as:
R. Daher, S. El Ouadih, (δ,γ)-Jacobi-Dunkl Lipschitz Functions in the Space L2(R,Aα,β(x)dx), Int. J. Anal. Appl., 8 (2) (2015), 123-129.

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.