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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2016, Volume 1, Issue 1, Pages 52–58
(Mi chfmj6)
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Mathematics
Hilbert's inequality generalization to $l_p$ spaces
M. G. Lepchinski Chelyabinsk State University, Chelyabinsk, Russia
Abstract:
A generalization to famous Hilbert's inequality is considered for the case of summable with $p$-th degree sequences ($p\leq 2$). New result is obtained by means of the operator approach. It is shown that the inequality can't be extended to the case $p>2$.
Keywords:
Hilbert's inequality, linear bounded operator, Minkowski's inequality integral form, function's rearrangements, integral inequality, Hardy — Littlewood inequality.
Received: 14.11.2015 Revised: 04.02.2016
Citation:
M. G. Lepchinski, “Hilbert's inequality generalization to $l_p$ spaces”, Chelyab. Fiz.-Mat. Zh., 1:1 (2016), 52–58
Linking options:
https://www.mathnet.ru/eng/chfmj6 https://www.mathnet.ru/eng/chfmj/v1/i1/p52
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Abstract page: | 149 | Full-text PDF : | 104 | References: | 27 |
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