We obtain new inequalities for the Fourier transform in the space , using a generalized spherical mean operator for proving two estimates in certain classes of functions characterized by a generalized continuity modulus.
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Radouan Daher 1; Mohamed El Hamma 1
@article{CRMATH_2014__352_3_235_0, author = {Radouan Daher and Mohamed El Hamma}, title = {On estimates for the {Fourier} transform in the space $ {L}^{2}({\mathbb{R}}^{n})$}, journal = {Comptes Rendus. Math\'ematique}, pages = {235--240}, publisher = {Elsevier}, volume = {352}, number = {3}, year = {2014}, doi = {10.1016/j.crma.2013.12.016}, language = {en}, }
TY - JOUR AU - Radouan Daher AU - Mohamed El Hamma TI - On estimates for the Fourier transform in the space $ {L}^{2}({\mathbb{R}}^{n})$ JO - Comptes Rendus. Mathématique PY - 2014 SP - 235 EP - 240 VL - 352 IS - 3 PB - Elsevier DO - 10.1016/j.crma.2013.12.016 LA - en ID - CRMATH_2014__352_3_235_0 ER -
Radouan Daher; Mohamed El Hamma. On estimates for the Fourier transform in the space $ {L}^{2}({\mathbb{R}}^{n})$. Comptes Rendus. Mathématique, Volume 352 (2014) no. 3, pp. 235-240. doi : 10.1016/j.crma.2013.12.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.016/
[1] Approximation of functions by Fourier–Bessel sums, Izv. Vysš. Učebn. Zaved., Mat., Volume 8 (2001), pp. 3-9
[2] Some remarks concerning the Fourier transform in the space , Comput. Math. Math. Phys., Volume 48 (2008) no. 12, pp. 2113-2120
[3] Growth properties of the Fourier transforms, Filomat, Volume 26 (2012) no. 4, pp. 755-760
[4] Growth properties of Fourier transforms via moduli of continuity, J. Funct. Anal., Volume 255 (2008), pp. 2265-2285
[5] Moduli of continuity and average decay of Fourier transform: Two sided estimates, Contemp. Math., Volume 458 (2008), pp. 377-392
[6] Approximation of Functions of Several Variables and Embedding Theorems, Nauka, Moscow, 1996 (in Russian)
[7] The Fourier transform of functions satisfying the Lipschitz condition on rank one symmetric spaces, Sib. Math. J., Volume 45 (2005) no. 6, pp. 1108-1118
[8] Introduction of the Theory of Fourier Integrals, Oxford University Press, 1937
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