Boundedness of hardy operator on variable exponenet lebesgue spaces

This postgraduate thesis deals with boundedness of Hardy operator in variable exponent Lebesgue spaces and related Hardy-type inequalities.In Chapter 1 an overview of development and application areas of Hardy operator and Hardy inequalities are mentioned.In Chapter 2 basic concepts and related theorems used in this thesis are described.In Chapter 3 Orlicz spaces ( ) and variable exponent Lebesgue spaces ( ) are discribed and some properties of variable exponent Lebesgue spaces are examined.In Chapter 4 before all else Hardy operators and Hardy inequalities in classical Lebesgue spaces ( ) are examined and then these are briefly represented in Orlicz spaces.In Chapter 5 the boundedness of Hardy operators and Hardy inequalities in variable exponent Lebesgue spaces are tried to express by the means of some studies.