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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 $\omega$ satisfying N. K. Bari's condition, we present a criterion for determining whether a function with a nonnegative MFT belongs to the class $H^\omega$.
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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\paper Weighted integrability of multiplicative Fourier transforms
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\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
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\pages 71--81
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 3 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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