Hardy inequalities and Hardy type operators

In this thesis, Hardy inequalities(Hardy-type inequalities) and Hardyoperators(Hardy-type operators) topics are dealt with and the boundedness of theRiemann-Liouville and Weyl operators from L_{v}^{p} to L_{w}^{q} is obtained.In the first chapter, we dealt with the history of the inequalities generally andmentioned the historical and theoretical development of Hardy inequalities and Hardyoperators.In the second chapter, we gave the basic and necessary informations for properlyunderstanding of following chapters.In the third chapter; measure, Lebesgue outer measure, Lebesgue integral andrelated topics which are the basic concepts of the Lebesgue theory are mentioned.In the fourth chapter, Lebesgue space and related concepts and theorems,moreover Sobolev space and imbeddings theorems are dealt with.In the fifth chapter, in their historical and theoretical development Hardyinequalities and Hardy operators are dealt with largely and explicitly.In the last chapter; first, Hardy-type operators are mentioned, then the necessaryand sufficient conditions are found for the weight pairs (v,w) which provide theboundedness of the Riemann-Liouville and Weyl operators from L_{v}^{p} to L_{w}^{q}.