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Hardy inequalities for $p$-weakly monotone functions
M. Saucedo Centre de Recerca Matematica, Edifici C, Bellaterra 08193, Spain
Abstract:
We prove Hardy-type inequalities
$$
\left(\int_d^\infty\left|\int_d^s f(x)dx\right|^p s^\beta ds\right)^{1/p}\leqslant C\left(\int_d^\infty|f(s)|^qs^\alpha ds\right)^{1/q}
$$
for the class of $p$-weakly monotone functions with $q$ or $p$ smaller than $1$ and $d\geqslant 0$.
Keywords and phrases:
Hardy-type inequality, generalized monotonicity.
Received: 16.01.2022 Revised: 24.03.2023
Citation:
M. Saucedo, “Hardy inequalities for $p$-weakly monotone functions”, Eurasian Math. J., 14:2 (2023), 94–106
Linking options:
https://www.mathnet.ru/eng/emj472 https://www.mathnet.ru/eng/emj/v14/i2/p94
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Abstract page: | 54 | Full-text PDF : | 24 | References: | 9 |
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