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

SOME NEW MULTIDIMENSIONAL HARDYTYPE INEQUALITIES WITH KERNELS VIA CONVEXITYJames A. Oguntuase and Philip DurojayeDepartment of Mathematics, University of Agriculture, P.M.B. 2240 Abeokuta, Nigeria and Department of Mathematics and Statistics, Federal Polytechnic, P.M.B. 50 Ilaro, NigeriaAbstract: We prove some new multidimensional Hardytype 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 onedimensional 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 2 Apr 2013. This page was last modified: 8 Apr 2013.
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