Geodesic
Hardy Inequality in Variable Exponent Lebesgue Spaces
Fractional calculus and applied analysis, Tome 10 (2007) no. 1, pp. 01-18.

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We prove the Hardy inequality and a similar inequality for the dual Hardy operator for variable exponent Lebesgue spaces.
Keywords: Hardy Inequalities, Hardy Operators, Variable Exponent, Generalized Lebesgue Spaces, Homogeneous Kernels, Convolution Operators, 26D10, 46E30, 47B38 
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Diening, Lars; Samko, Stefan. Hardy Inequality in Variable Exponent Lebesgue Spaces. Fractional calculus and applied analysis, Tome 10 (2007) no. 1, pp. 01-18. http://geodesic.mathdoc.fr/item/FCAA_2007_10_1_a0/