Abstract
In this paper, we prove the generalization of Titchmarsh’s theorem for the Fourier transform for functions satisfying the \((n,\alpha )\)-Fourier Lipschitz condition in the space \(\mathrm {L}^{2}(\mathbb {R}^{n})\).
Similar content being viewed by others
References
Abouelaz, A., Daher, R., El Hamma, M.: Fourier transform of Dini-Lipschitz functions in the Space \({\rm L}^{2}(\mathbb{R}^{{\rm n}}\), Roma. J. Math. Comput. Sci., 3(1), 41–47 (2013)
Abouelaz, A., Daher, R., El Hamma, M.: Generalization of Titchmarsh’s theorem for the Jacobi transform. FACTA UNIVERSITATIS (NIS) Ser. Math. Inform. 28(1), 43–51 (2013)
Belkina, E.S., Platonov, S.S.: Equivalence of K-functionnals and modulus of smoothness constructed by generalized Dunkl translations. Izv. Vyssh. Uchebn. Zaved. Mat. 8, 3–15 (2008)
Bray, W.O., Pinsky, M.A.: Growth properties of Fourier transforms via moduli of continuity. J. Funct. Anal. 255, 2265–2285 (2008)
Daher, R., El Hamma, M.: Bessel transform of \((k,\gamma )\)-Bessel Lipschitz functions. J. Math. (2013) (article ID 418546)
Daher, R., El Hamma, M.: On estimates for the Fourier transform in the space \(^{2}(\mathbb{R}^{n})\). C. R. Acad. Sci. Paris, Ser. I, 352, 235–240 (2014)
Titchmarsh, E.C.: Introduction of the theory of Fourier integrals. Oxford University Press, Oxford (1937)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor François Rouvière for his 70’s birthday.
Rights and permissions
About this article
Cite this article
Daher, R., Boujeddaine, M. & Hamma, M.E. Generalization of Titchmarsh’s theorem for the Fourier transform in the Space \(\mathrm {L}^{2}(\mathbb {R}^{n})\) . Afr. Mat. 27, 753–758 (2016). https://doi.org/10.1007/s13370-015-0368-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-015-0368-x