Open AccessOn Holder’s Inequality in Lebesgue Spaces with Variable Order of Summability
Author(s) -
В. И. Буренков,
В. И. Буренков,
Tamara Tararykova,
Tamara Tararykova
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-3-472-482
Subject(s) - lp space , mathematics , norm (philosophy) , lebesgue integration , pure mathematics , inequality , standard probability space , hölder's inequality , order (exchange) , lebesgue's number lemma , variable (mathematics) , discrete mathematics , mathematical analysis , linear inequality , banach space , riemann integral , operator theory , economics , epistemology , finance , fourier integral operator , philosophy
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 Holders inequality for such spaces, which is more general and more precise than those known earlier.