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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2022 Volume 319, Pages 94–105 (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

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.

UDC: 517.518.5+517.444

Received: August 16, 2021
Revised: December 11, 2021
Accepted: December 24, 2021

DOI: 10.4213/tm4252


 English version: Proceedings of the Steklov Institute of Mathematics, 2022, 319, 85–96

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© Steklov Math. Inst. of RAS, 2025