Some Remarks Concerning the Jacobi-Dunkl Transform in the Space Lp(R,Aα,β(t)dt)

Article Sidebar

PDF
Cite as:
R. Daher, S. El Ouadih, A. Belkhadir, Some Remarks Concerning the Jacobi-Dunkl Transform in the Space Lp(R,Aα,β(t)dt), Int. J. Anal. Appl., 8 (2) (2015), 104-109.

Main Article Content

R. Daher, S. El Ouadih, A. Belkhadir

Abstract

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the (φ,p)-Lipschitz Jacobi-Dunkl condition in the   space Lp(R,Aα,β(t)dt),α ≥ β ≥-1/2, α≠-1/2.

Article Details

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. Johansen. T. R, Remarks on the inverse cherednik-opdam transform on the real line, arxiv: 1502.01293v1 (2015).
  7. Koornwinder. T. H , A new proof of a Paley-Wiener type theorems for the Jacobi transform , Ark.Math.13(1975), 145-159.
  8. Titchmarsh. E. C, Introduction to the theory of Fourier integrals , Claredon, Oxford. (1948), Komkniga, Moscow, (2005).