Boundedness of hardy operator in l^p spaces

After the introduction part of this thesis, in the second part (Resource Research), the basic concepts and theorems of functional analysis and real analysis, which have an important place in the analysis we will need throughout our research, are explained. In the third chapter (Materials and Methods), basic inequalities and important inequalities related to Hardy's inequality are explained. In the fourth chapter (Research Results and Discussion), considering the Hilbert inequality and Hardy type inequalities in l^p spaces for p≥1, has been investigated, so researched boundedness and are continuity of the discrete Godfrey Harold Hardy operator and its Dual operator. Finally, in the fifth chapter (Results and Recommendations), the results and recommendations of our litareture research are explained.