Abstract
In this paper, we introduce a new version of the definition of a quasinorm (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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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 3, In honor of the 70th anniversary of Professor V. M. Filippov, 2021.
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Burenkov, V.I., Tararykova, T.V. On Holder’s Inequality in Lebesgue Spaces with Variable Order of Summability. J Math Sci 278, 254–263 (2024). https://doi.org/10.1007/s10958-024-06918-3
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DOI: https://doi.org/10.1007/s10958-024-06918-3