James Oguntuase

MULTIDIMENSIONAL HARDY-TYPE INEQUALITIES VIA CONVEXITY

Let an almost everywhere positive function Φ be convex for p >1 and p p ∈(0,1), and such that Ax p ≤Φ( x )≤ Bx p holds on for some positive constants A ≤ B . In this paper we derive a class of general integral multidimensional Hardy-type inequalities with power weights, whose left-hand sides involve instead of , while the corresponding right-hand sides remain as in the classical Hardy’s inequality and have explicit constants in front of integrals. We also prove the related dual inequalities. The relations obtained are new even for the one-dimensional case and they unify and extend several inequalities of Hardy type known in the literature.

Refinements of some limit hardy-Type Inequalities via Superquadracity

Refinements of some limit Hardy-type inequalities are derived anddiscussed using the concept of superquadracity. We also proved that all threeconstants appearing in the refined inequalities obtaine ...

Refinements of Hardy-type inequalities via superquadracity

Some new refinements of Hardy-type integral inequalities are derived, proved and discussed using the concept of superquadratic and subquadratic functions. The results obtained are generalizations and improvements of inequalities of this type in the literature.