Geodesic
Inequalities for weighted Hardy operators in weighted variable exponent Lebesgue space with $0 p(x) 1$
Eurasian mathematical journal, Tome 9 (2018) no. 1, pp. 30-39

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Weighted inequalities are proved for the weighted Hardy operators and the weighted dual of the classical Hardy operator acting from one weighted variable exponent Lebesgue space $L_{p(.),\omega_1} (0,\infty)$ to another weighted variable exponent Lebesgue space $L_{p(.),\omega_2} (0,\infty)$ for $0 p(x) \leqslant q(x) 1$. 
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     author = {S. A. Bendaoud and A. Senouci},
     title = {Inequalities for weighted {Hardy} operators in weighted variable exponent {Lebesgue} space with $0 < p(x) < 1$},
     journal = {Eurasian mathematical journal},
     pages = {30--39},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2018_9_1_a2/}
}
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S. A. Bendaoud; A. Senouci. Inequalities for weighted Hardy operators in weighted variable exponent Lebesgue space with $0 < p(x) < 1$. Eurasian mathematical journal, Tome 9 (2018) no. 1, pp. 30-39. http://geodesic.mathdoc.fr/item/EMJ_2018_9_1_a2/