Geodesic
Some New Multidimensional Hardy-type Inequalities With Kernels Via Convexity
Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 153 .

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We prove some new multidimensional Hardy-type inequalities involving general Hardy type operators with positive kernels for functions $\phi$ which may not necessarily be convex but satisfy the condition $A\psi(\x)\leq\phi(\x)\leq B\psi(\x)$, where $\psi $ is convex. Our approach is mainly the use of convexity argument and the results obtained are new even for the one-dimensional case and also unify and extend several inequalities of Hardy type known in the literature.
Classification : 26D10 26D15
Keywords: Multidimensional Hardy type inequalities, convexity argument, general Hardy type operator, kernels, weight functions 
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     author = {James A. Oguntuase and Philip Durojaye},
     title = {Some {New} {Multidimensional} {Hardy-type} {Inequalities} {With} {Kernels} {Via} {Convexity}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {153 },
     publisher = {mathdoc},
     volume = {_N_S_93},
     number = {107},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2013_N_S_93_107_a12/}
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James A. Oguntuase; Philip Durojaye. Some New Multidimensional Hardy-type Inequalities With Kernels Via Convexity. Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 153 . http://geodesic.mathdoc.fr/item/PIM_2013_N_S_93_107_a12/