Establishment of some properties of weighted inequalities of hardy-type

In this research various generalizations of the Hardy-inequality are made. The new results on weighted norm inequalities of Hardy-type are obtained using the concept of formal adjoint operators. Standard preliminary results have been given in seven theorems, including lemmas and corollaries which pave the way to the main results. The main results are given in five theorems together with their consequences. The necessary and sufficient conditions for the weighted Hardy inequality to hold are obtained using functional analytic techniques. Furthermore, the roundedness of the Hardy operator and the best possible constants in the weighted Hardy inequalities are obtained. The results of this dissertation give an insight on the possible areas of future research and applications of this inequality in solving different equations and in obtaining numerical solutions of boundary-value problems