Geodesic
On Holder's inequality in Lebesgue spaces with variable order of summability
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 472-482 
V. I. Burenkov; T. V. Tararykova. On Holder's inequality in Lebesgue spaces with variable order of summability. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 472-482. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a4/
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     author = {V. I. Burenkov and T. V. Tararykova},
     title = {On {Holder's} inequality in {Lebesgue} spaces with variable order of summability},
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     volume = {67},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we introduce a new version of the definition of a quasi-norm (in particular, a norm) in Lebesgue spaces with variable order of summability. Using it, we prove an analogue of Hölder's inequality for such spaces, which is more general and more precise than those known earlier.

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