DINI LIPSCHITZ FUNCTIONS FOR THE GENERALIZED FOURIER-DUNKL TRANSFORM IN THE SPACE $L_{\alpha,n}^{2}$

Year 2017, Volume: 5 Issue: 1, 92 - 98, 01.04.2017

S. El Ouadıh , R. Daher , M. El Hamma

https://izlik.org/JA42NX23MN

Abstract

Using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [5] for the generalized Fourier-Dunkl transform for functions satisfying the Fourier-Dunkl Dini Lipschitz condition in the space $L_{\alpha,n}^{2}$.

Keywords

Differential-difference operator , Generalized Fourier-Dunkl transform , Generalized translation operator.

References

• [1] Al Sadhan, S.A., Al Subaie, R.F. and Mourou, M.A. 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] Dunkl, C.F. Differential-Difference Operators Associated to Reflection Groups. Transactions of the American Mathematical Society, 311,(1989), 167-183.
• [4] Dunkl, C.F. Hankel Transforms Associated to Finite Reflection Groups. Contemporary Mathematics, 138,(1992), 128- 138.
• [5] Younis M.S. Fourier transforms of Dini-Lipschitz Functions. Int. J. Math. Math. Sci. 9 (2),(1986), 301312. doi:10.1155/S0161171286000376.
• [6] Al Subaie, R.F. and Mourou, M.A. Inversion of Two Dunkl Type Intertwining Operators on R Using Generalized Wavelets. Far East Journal of Applied Mathematics, 88,(2014), 91-120.