EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 93(107), pp. 153–164 (2013)

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SOME NEW MULTIDIMENSIONAL HARDY-TYPE INEQUALITIES WITH KERNELS VIA CONVEXITY

James A. Oguntuase and Philip Durojaye

Department of Mathematics, University of Agriculture, P.M.B. 2240 Abeokuta, Nigeria and Department of Mathematics and Statistics, Federal Polytechnic, P.M.B. 50 Ilaro, Nigeria

Abstract: 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.

Keywords: Multidimensional Hardy type inequalities, convexity argument, general Hardy type operator, kernels, weight functions

Classification (MSC2000): 26D10; 26D15

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Electronic fulltext finalized on: 2 Apr 2013. This page was last modified: 8 Apr 2013.

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