Geodesic
Uniform Convergence and Integrability of Multiplicative Fourier Transforms
Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 44-60

Voir la notice de l'article provenant de la source Math-Net.Ru

For multiplicative Fourier transforms, analogs of results obtained by R. P. Boas, F. Moricz, M. I. D'yachenko, I. P. Liflyand, and S. Yu. Tikhonov and dealing with conditions for the uniform convergence and weighted integrability with power weight of classical Fourier transforms as well as conditions for these transforms to belong to Lipschitz classes are proved. Certain results of C. W. Onneweer concerning conditions for multiplicative Fourier transforms to belong to Lipschitz–Besov and Herz spaces are also generalized.
Mots-clés : multiplicative Fourier transform
Keywords: weighted integrability of Fourier transforms, Lipschitz class, Lipschitz–Besov space, Herz space, Dirichlet kernel, Hölder's inequality, Hardy's inequality, Minkowski's inequality. 
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     author = {S. S. Volosivets and B. I. Golubov},
     title = {Uniform {Convergence} and {Integrability} of {Multiplicative} {Fourier} {Transforms}},
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S. S. Volosivets; B. I. Golubov. Uniform Convergence and Integrability of Multiplicative Fourier Transforms. Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 44-60. http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a3/