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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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/

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