Hardy inequalities and some upplications

In this thesis, information about Lebesgue space, Hardy inequalities andsome applications of Hardy inequalities will be given.In the rst chapter, we will give information about some space knowledge,denition of Lebesgue space and it's basic properties, which is very important forthe other sections. Moreover, we will give information about Lp space, it's normand it's basic properties.In the second chapter, we talk about the beginning of Hardy inequality,developing of Hardy inequality from beginning to today, Hardy's inequalities' theother forms and necessary and sucient conditions for realize the Hardy inequal-ity.In the third chapter, applications will be given.