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Mat. Zametki, 2015, Volume 98, Issue 1, Pages 44–60 (Mi mz10691)  

This article is cited in 1 scientific paper (total in 1 paper)

Uniform Convergence and Integrability of Multiplicative Fourier Transforms

S. S. Volosivetsa, B. I. Golubovb

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1520.2014/K
Russian Foundation for Basic Research 14-01-00417
The work of the first author was supported by the Ministry of Education and Science of the Russian Federation (grant no. 1.1520.2014/K). The work of the second author was supported by the Russian Foundation for Basic Research (grant no. 14-01-00417) and by the program "Contemporary Problems of Analysis and Mathematical Physics" of the Ministry of Education and Science of the Russian Federation.


DOI: https://doi.org/10.4213/mzm10691

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English version:
Mathematical Notes, 2015, 98:1, 53–67

Bibliographic databases:

UDC: 517.518
Received: 27.09.2014

Citation: S. S. Volosivets, B. I. Golubov, “Uniform Convergence and Integrability of Multiplicative Fourier Transforms”, Mat. Zametki, 98:1 (2015), 44–60; Math. Notes, 98:1 (2015), 53–67

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. I. Golubov, S. S. Volosivets, “Integrability and uniform convergence of multiplicative transforms”, New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics, eds. P. Dang, M. Ku, T. Qian, L. Rodino, Birkhauser Boston, 2017, 363–369  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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