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.