Some New Multidimensional Hardy-type Inequalities with Kernels via Convexity

Abstract

We prove some new multidimensional Hardy-type inequalities involving general Hardy type operators with positive kernels for functions φ which may not necessarily be convex but satisfy the condition Aψ(x) 6 φ(x) 6 Bψ(x), where ψ 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.

Cite this paper

@inproceedings{Oguntuase2013SomeNM, title={Some New Multidimensional Hardy-type Inequalities with Kernels via Convexity}, author={J. A. Oguntuase and Philip Durojaye and Stevan Pilipovic}, year={2013} }