JACOBI TRANSFORM OF \((\nu, \gamma, p)\)-JACOBI–LIPSCHITZ FUNCTIONS IN THE SPACE \(\mathrm{L}^{p}(\mathbb{R}^{+},\Delta_{(\alpha,\beta)}(t) dt)\)

Mohamed El Hamma     (Laboratoire TAGMD, Faculté des Sciences Aïn Chock, Université Hassan II, B.P 5366 Maarif, Casablanca, Morocco)
Hamad Sidi Lafdal     (CRMEF, Laayoune, Morocco)
Nisrine Djellab     (Laboratoire TAGMD, Faculté des Sciences Aïn Chock, Université Hassan II, B.P 5366 Maarif, Casablanca, Morocco)
Chaimaa Khalil     (Laboratoire TAGMD, Faculté des Sciences Aïn Chock, Université Hassan II, B.P 5366 Maarif, Casablanca, Morocco)

Abstract


Using a generalized translation operator, we obtain an analog of Younis' theorem [Theorem 5.2, Younis M.S. Fourier transforms of Dini–Lipschitz functions, Int. J. Math. Math. Sci., 1986] for the Jacobi transform for functions from the \((\nu, \gamma, p)\)-Jacobi–Lipschitz class in the space \(\mathrm{L}^{p}(\mathbb{R}^{+},\Delta_{(\alpha,\beta)}(t)dt)\).


Full Text:

PDF

References


  1. Anker J.-P., Damek E. and Yacoub C. Spherical analysis on harmonic \(AN\) groups. Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 1996. Vol. 23, No. 4. P. 643–679. URL: http://www.numdam.org/item/ASNSP_1996_4_23_4_643_0/
  2. Bray W.O., Pinsky M.A. Growth properties of Fourier transforms via moduli of continuity. J. Funct. Anal., 2008. Vol. 255, No. 9. P. 2265–2285. DOI: 10.1016/j.jfa.2008.06.017
  3. Chokri A., Jemai A. Integrability theorems for Fourier–Jacobi transform. J. Math. Inequal., 2012. Vol. 6, No. 3. P. 343–353. DOI: 10.7153/jmi-06-34
  4. Daher R., El Hamma M. Some estimates for the Jacobi transform in the space \(\mathrm{L}^{2} (\mathbb{R}^{+}, \Delta_{(\alpha,\beta)}(t)dt)\). Int. J. Appl. Math., 2012. Vol. 25, No. 1. P. 13–24.
  5. Flensted-Jensen M., Koornwinder T.H. The convolution structure for Jacobi expansions. Ark. Mat., 1973. Vol. 11, No. 1–2. P. 245–262. DOI: 10.1007/BF02388521
  6. Koornwinder T.H. Jacobi functions and analysis on noncompact semisimple Lie groups. In: Special Functions: Group Theoretical Aspect and Applications. R.A. Askey et al. (eds.) Mathematics and its Applications, vol. 18. Dordrecht: Springer, 1984. P. 1–85. DOI: 10.1007/978-94-010-9787-1_1
  7. Platonov S.S. Approximation of functions in \(\mathrm{L}_{2}\)-metric on noncompact symmetric spaces of rank 1. Algebra i Analiz, 1999. Vol. 11, No. 1. P. 244–270.
  8. Younis M.S. Fourier transforms of Dini–Lipschitz functions. Int. J. Math. Math. Sci., 1986. Vol. 9, No. 2. P. 301–312. DOI: 10.1155/S0161171286000376



DOI: http://dx.doi.org/10.15826/umj.2019.1.006

Article Metrics

Metrics Loading ...

Refbacks

  • There are currently no refbacks.