Geodesic
Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 94-105

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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. 
@article{TRSPY_2022_319_a7,
     author = {B. I. Golubov and S. S. Volosivets},
     title = {Fourier {Transforms} of {Convolutions} of {Functions} in {Lebesgue} and {Lorentz} {Spaces}},
     journal = {Informatics and Automation},
     pages = {94--105},
     publisher = {mathdoc},
     volume = {319},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a7/}
}
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B. I. Golubov; S. S. Volosivets. Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 94-105. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a7/