Boundedness of classical operators and their commutators on vanishing morrey spaces

This thesis consists of five main sections. The first section, is devoted to introduction. In the second section the basic definitons and important theorems are involved and the operators and the commutators which we have studied are defined. In the third section both classical and the generalized Morrey subspaces are appeared and some special theorems and key features which are used on these spaces are detailed. The fourth section consists of four subsections. In the first part the boundedness of the classical operators which we studied are proved on the Vanishing Morrey spaces. In the second part the results which we obtained in the Vanishing generalized Morrey spaces are involved. In the third part the boundedness of the commutators of the Maximal and the fractional maximal operators are proved on the Vanishing generalized Morrey spaces. In the fourth part weighted Vanishing generalized Morrey spaces are defined and the boundedness of the classical operators and their commutators are proved in these spaces. Finally in the fifth section the results which we obtained are analyzed