×

On estimates for the Fourier transform in the space \(L^{2}(\mathbb{R}^{n})\). (English. French summary) Zbl 1286.43005

Summary: We obtain new inequalities for the Fourier transform in the space \(L^{2}(\mathbb{R}^{n})\), using a generalized spherical mean operator for proving two estimates in certain classes of functions characterized by a generalized continuity modulus.

MSC:

43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abilov, V. A.; Abilova, F. V., Approximation of functions by Fourier-Bessel sums, Izv. Vysš. Učebn. Zaved., Mat., 8, 3-9 (2001) · Zbl 1029.42023
[2] Abilov, V. A.; Abilova, M. V.; Kerimov, M. K., Some remarks concerning the Fourier transform in the space \(L_2(R^n)\), Zh. Vychisl. Mat. Mat. Fiz.. Zh. Vychisl. Mat. Mat. Fiz., Comput. Math. Math. Phys., 48, 12, 2146-2153 (2008) · Zbl 1164.42307
[3] Bray, W. O.; Pinsky, M. A., Growth properties of the Fourier transforms, Filomat, 26, 4, 755-760 (2012) · Zbl 1289.42031
[4] Bray, W. O.; Pinsky, M. A., Growth properties of Fourier transforms via moduli of continuity, J. Funct. Anal., 255, 2265-2285 (2008) · Zbl 1159.42006
[5] Gioev, D., Moduli of continuity and average decay of Fourier transform: Two sided estimates, Contemp. Math., 458, 377-392 (2008) · Zbl 1268.42013
[6] Nikol’skii, S. M., Approximation of Functions of Several Variables and Embedding Theorems (1996), Nauka: Nauka Moscow, (in Russian)
[7] Platonov, S. S., The Fourier transform of functions satisfying the Lipschitz condition on rank one symmetric spaces, Sib. Math. J., 45, 6, 1108-1118 (2005)
[8] Titchmarsh, E. C., Introduction of the Theory of Fourier Integrals (1937), Oxford University Press · JFM 63.0367.05
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.