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Chelyab. Fiz.-Mat. Zh., 2016, Volume 1, Issue 1, Pages 52–58 (Mi chfmj6)  

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.

Full text: PDF file (675 kB)
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UDC: 517.9
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

Citation in format AMSBIB
\Bibitem{Lep16}
\by M.~G.~Lepchinski
\paper Hilbert's inequality generalization to $l_p$ spaces
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2016
\vol 1
\issue 1
\pages 52--58
\mathnet{http://mi.mathnet.ru/chfmj6}
\elib{https://elibrary.ru/item.asp?id=27541606}


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