Geodesic
Hilbert's inequality generalization to $l_p$ spaces
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 1, pp. 52-58

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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. 
@article{CHFMJ_2016_1_1_a5,
     author = {M. G. Lepchinski},
     title = {Hilbert's inequality generalization to $l_p$ spaces},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {52--58},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_1_a5/}
}
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M. G. Lepchinski. Hilbert's inequality generalization to $l_p$ spaces. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 1, pp. 52-58. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_1_a5/