Characterization of (δ,γ)-Dini-Lipschitz Functions in Terms of Their Jacobi-Dunkl Transforms

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A. Belkhadir, A. Abouelaz, R. Daher, Characterization of (δ,γ)-Dini-Lipschitz Functions in Terms of Their Jacobi-Dunkl Transforms, Int. J. Anal. Appl., 9 (2) (2015), 142-150.

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A. Belkhadir, A. Abouelaz, R. Daher

Abstract

In this paper, we are going to define a generalized Dini-Lipschitz class and give a characterization for functions belonging to by means of an asymptotic estimating growth of the norm of their Jacobi-Dunkl transforms.

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References

  1. A. Belkhadir, A. Abouelaz, and R. Daher, An analog of Titchmarsh's theorem for the JacobiDunkl transform in the space L2 α,β(R), International Journal of Analysis and Applications, 8(1) (2015), 15-21.
  2. A. Belkhadir and A. Abouelaz, Generalization of Titchmarsh's theorem for the Jacobi-Dunkl transform, Gen. Math. Notes, 28(2) (2015), 9-20.
  3. M. S. Younis, Fourier Transforms of Dini-Lipschitz functions, International Journal of Mathematics and Mathematical Sciences, 9(2) (1986), 301-312.
  4. H.B. Mohamed and H. Mejjaoli, Distributional Jacobi-Dunkl transform and application, Afr. Diaspora J. Math, (2004), 24-46.
  5. H.B. Mohamed, The Jacobi-Dunkl transform on R and the convolution product on new spaces of distributions, Ramanujan J., 21(2010), 145-175.
  6. N.B. Salem and A.O.A. Salem, Convolution structure associated with the Jacobi-Dunkl operator on R , Ramanujan J., 12(3) (2006), 359-378.
  7. N.B. Salem and A.O.A. Salem, Sobolev types spaces associated with the Jacobi-Dunkl operator, Fractional Calculus and Applied Analysis, 7(1) (2004), 37-60.
  8. W.O. Bray and M.A. Pinsky, Growth properties of Fourier transforms via moduli of continuity, Journal of Functional Analysis, 255(2008), 2256-2285.
  9. F. Chouchane, M. Mili and K. Trim`eche, Positivity of the intertwining opertor and harmonic analysis associated with the Jacobi-Dunkl operator on R, J. Anal. Appl., 1(4) (2003), 387-412.
  10. T.H. Koornwinder, Jacobi functions and analysis on noncompact semi-simple Lie groups, In: R.A. Askey, T.H. Koornwinder and W. Schempp (eds.), Special Functions: Group Theoritical Aspects and Applications, D. Reidel, Dordrecht, (1984).
  11. T.H. Koornwinder, A new proof of a Paley-Wiener type theorems for the Jacobi transform, Ark. Math., 13(1975), 145-159.
  12. S.S. Platonov, Approximation of functions in L2-metric on noncompact rank 1 symetric spaces, Algebra Analiz., 11(1) (1999), 244-270.
  13. E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Claredon, Oxford, (1948), Komkniga, Moscow, (2005).