| Characterization of $(\eta,\gamma,k,2)$-Dini-Lipschitz functions in terms of their Helgason Fourier transform |
| Radouan Daher and Salah El Ouadih |
Abstract In this paper, using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [M. S. Younis, Fourier transforms of Dini-Lipschitz functions, Int. J. Math. Math. Sci. 9 (2),(1986), 301--312.] for the Helgason Fourier transform of a set of functions satisfying the $(\eta,\gamma,k,2)$-Dini-Lipschitz condition in the space $L^{2}$ for functions on noncompact rank one Riemannian symmetric spaces.
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Keywords: symmetric space; Helgason Fourier transform; Lipschitz condition; generalized translation operator. |
MSC: 42B37 |
Pages: 267$-$276 |
Volume 68 , Issue 4 , 2016 |
