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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 269, Pages 71–81 (Mi tm2899)  
This article is cited in 3 scientific papers (total in 3 papers)

Weighted integrability of multiplicative Fourier transforms

S. S. Volosivetsa, B. I. Golubovb

a Mechanics and Mathematics Department, Saratov State University, Saratov, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, Russia
Full-text PDF (223 kB) Citations (3)
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Abstract: We study the relationship between the weighted integrability of a function and that of its multiplicative Fourier transform (MFT). In particular, for the MFT we prove an analog of R. Boas' conjecture related to the Fourier sine and cosine transforms. In addition, we obtain a sufficient condition under which a contraction of an MFT is also an MFT. For the moduli of continuity ω satisfying N. K. Bari's condition, we present a criterion for determining whether a function with a nonnegative MFT belongs to the class Hω.
Received in December 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 269, Pages 65–75
DOI: https://doi.org/10.1134/S0081543810020069
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: S. S. Volosivets, B. I. Golubov, “Weighted integrability of multiplicative Fourier transforms”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Trudy Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 71–81; Proc. Steklov Inst. Math., 269 (2010), 65–75
Citation in format AMSBIB
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\by S.~S.~Volosivets, B.~I.~Golubov
\paper Weighted integrability of multiplicative Fourier transforms
\inbook Function theory and differential equations
\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2010
\vol 269
\pages 71--81
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
  • https://www.mathnet.ru/eng/tm2899
  • https://www.mathnet.ru/eng/tm/v269/p71
    • This publication is cited in the following 3 articles:
    1. Golubov B.I., Volosivets S.S., “Integrability and Uniform Convergence of Multiplicative Transforms”, New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics, eds. Dang P., Ku M., Qian T., Rodino L., Birkhauser Boston, 2017, 363–369  crossref  mathscinet  zmath  isi
    2. Mukanov A., “Boas' Conjecture in Anisotropic Lebesgue and Lorentz Spaces”, Acta Sci. Math., 83:1-2 (2017), 201–214  crossref  mathscinet  zmath  isi  scopus
    3. S. S. Volosivets, B. I. Golubov, “Uniform Convergence and Integrability of Multiplicative Fourier Transforms”, Math. Notes, 98:1 (2015), 53–67  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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