S. S. Volosivets, B. I. Golubov, “Uniform Convergence and Integrability of Multiplicative Fourier Transforms”, Mat. Zametki, 2015, Volume 98, Issue 1,Pages <nobr>44

This article is cited in 1 paper

Uniform Convergence and Integrability of Multiplicative Fourier Transforms

S. S. Volosivets^a, B. I. Golubov^b

^a Saratov State University named after N. G. Chernyshevsky
^b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: 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.

Keywords: multiplicative Fourier transform, weighted integrability of Fourier transforms, Lipschitz class, Lipschitz–Besov space, Herz space, Dirichlet kernel, Hölder's inequality, Hardy's inequality, Minkowski's inequality.

UDC: 517.518

Received: 27.09.2014

DOI: 10.4213/mzm10691