Geodesic
Hardy inequalities for $p$-weakly monotone functions
Eurasian mathematical journal, Tome 14 (2023) no. 2, pp. 94-106

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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 $d\geqslant 0$. 
@article{EMJ_2023_14_2_a5,
     author = {M. Saucedo},
     title = {Hardy inequalities for $p$-weakly monotone functions},
     journal = {Eurasian mathematical journal},
     pages = {94--106},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2023_14_2_a5/}
}
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M. Saucedo. Hardy inequalities for $p$-weakly monotone functions. Eurasian mathematical journal, Tome 14 (2023) no. 2, pp. 94-106. http://geodesic.mathdoc.fr/item/EMJ_2023_14_2_a5/