Dunkl Lipschitz functions for the Generalized Fourier-Dunkl Transform in the Space L2

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R. Daher, S. El Ouadih, M. El Hamma, Dunkl Lipschitz functions for the Generalized Fourier-Dunkl Transform in the Space L2, Int. J. Anal. Appl., 9 (1) (2015), 39-44.

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R. Daher, S. El Ouadih, M. El Hamma

Abstract

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Dunkl transform in the space L2 on certainclasses of functions.

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References

  1. S. A. Al Sadhan, R. F. Al Subaie and M. A. Mourou, Harmonic Analysis Associated with A First-Order Singular Differential-Difference Operator on the Real Line. Current Advances in Mathematics Research, 1(2014), 23-34.
  2. E. S. Belkina and S. S. Platonov, Equivalence of K-Functionnals and Modulus of Smoothness Constructed by Generalized Dunkl Translations, Izv. Vyssh. Uchebn. Zaved. Mat., 8(2008), 3-15.
  3. C. F. Dunkl, Differential-Difference Operators Associated to Reflection Groups. Transactions of the American Mathematical Society, 311(1989), 167-183.
  4. S. S. Platonov, The Fourier Transform of Function Satisfying the Lipshitz condition on rank 1 symetric spaces , Siberian Math.J.46(2005), 1108-1118.
  5. E. C. Titchmarsh , Introduction to the Theory of Fourier Integrals . Claredon , oxford, 1948, Komkniga.Moxow. 2005.
  6. R. F. Al Subaie and M. A. Mourou, Inversion of Two Dunkl Type Intertwining Operators on R Using Generalized Wavelets. Far East Journal of Applied Mathematics, 88(2014), 91-120.
  7. C. F. Dunkl, Hankel Transforms Associated to Finite Reflection Groups. Contemporary Mathematics, 138(1992), 128-138.