Geodesic
Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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{TM_2022_319_a7,
     author = {B. I. Golubov and S. S. Volosivets},
     title = {Fourier {Transforms} of {Convolutions} of {Functions} in {Lebesgue} and {Lorentz} {Spaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {94--105},
     publisher = {mathdoc},
     volume = {319},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_319_a7/}
}
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B. I. Golubov; S. S. Volosivets. Fourier Transforms of Convolutions of Functions in Lebesgue and Lorentz Spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 94-105. http://geodesic.mathdoc.fr/item/TM_2022_319_a7/