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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 319, Pages 94–105
DOI: https://doi.org/10.4213/tm4252 (Mi tm4252) 		 
Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces

B. I. Golubova, S. S. Volosivetsb

a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
b Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia
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DOI: https://doi.org/10.4213/tm4252
Abstract: We present conditions for weighted integrability of the Fourier transforms of convolutions of functions in Lorentz and Lebesgue spaces. We also obtain quantitative estimates related to this integrability. The results are shown to be sharp.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSRR-2020-0006
The work of the second author was supported by the Ministry of Science and Higher Education of the Russian Federation within the state assignment, project no. FSRR-2020-0006.
Received: August 16, 2021
Revised: December 11, 2021
Accepted: December 24, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 319, Pages 85–96
DOI: https://doi.org/10.1134/S008154382205008X
Bibliographic databases:
Document Type: Article
UDC: 517.518.5+517.444
Language: Russian
Citation: B. I. Golubov, S. S. Volosivets, “Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces”, Approximation Theory, Functional Analysis, and Applications, Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin, Trudy Mat. Inst. Steklova, 319, Steklov Math. Inst., Moscow, 2022, 94–105; Proc. Steklov Inst. Math., 319 (2022), 85–96
Citation in format AMSBIB
\Bibitem{GolVol22}
\by B.~I.~Golubov, S.~S.~Volosivets
\paper Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces
\inbook Approximation Theory, Functional Analysis, and Applications
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 319
\pages 94--105
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4252}
\crossref{https://doi.org/10.4213/tm4252}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563387}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 319
\pages 85--96
\crossref{https://doi.org/10.1134/S008154382205008X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85148478190}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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