Geodesic
Exact Calculation of Sums of the Lorentz Spaces~$\Lambda^{\alpha}$ and Applications
Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 649-658

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The norm on the sum of Lorentz spaces endowed with norms equal to the products of the classical norm by some numbers is exactly calculated. The obtained result makes it possible to prove an extrapolation theorem for collections of Lorentz, Lebesgue, and Marcinkiewicz spaces with a sharp constant.
Keywords: sum of Lorentz spaces, extrapolation theorems. 
@article{MZM_2018_104_5_a1,
     author = {E. I. Berezhnoi},
     title = {Exact {Calculation} of {Sums} of the {Lorentz} {Spaces~}$\Lambda^{\alpha}$ and {Applications}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {649--658},
     publisher = {mathdoc},
     volume = {104},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a1/}
}
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E. I. Berezhnoi. Exact Calculation of Sums of the Lorentz Spaces~$\Lambda^{\alpha}$ and Applications. Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 649-658. http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a1/