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) φ(x) 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.