Geodesic
Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces
Eurasian mathematical journal, Tome 8 (2017) no. 1, pp. 58-66

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The classical Hausdorff–Young and Hardy–Littlewood–Stein inequalities, relating functions on $\mathbb{R}$ and their Fourier transforms, are extended and complemented in various ways. In particular, a variant of the Hardy–Littlewood–Stein inequality covering the case $p\geqslant2$ is proved and two-sided estimates are derived. 
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     author = {A. N. Kopezhanova},
     title = {Some new inequalities for the {Fourier} transform for functions in generalized {Lorentz} spaces},
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A. N. Kopezhanova. Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces. Eurasian mathematical journal, Tome 8 (2017) no. 1, pp. 58-66. http://geodesic.mathdoc.fr/item/EMJ_2017_8_1_a5/