Boundedness Of Singular Integral Operators On Two Classes Of Spaces With Variable Exponent

In this thesis, we mainly study the boundedness of some operators and commuta-tors on Herz type spaces with variable exponent and Morrey type spaces with variable exponent. Firstly, we obtain the boundedness of commutators generated by Hardy type operators and BMO function, Lipschitz function on Herz and Herz-Morrey spaces with variable exponent by the method of studying ring decomposition of functions and equivalent estimation of the norm of ball on variable exponent spaces. Secondly, we prove the boundedness of Hardy type operators on variable exponent Herz spaces by the similar method as before. Finally, we introduce a new function space that is Morrey spaces with variable exponents related to certain nonnegative potentials and consider the boundedness of some Schrodinger type operators and commutators on Morrey spaces with variable exponent related to certain nonnegative potentials by the boundedness of operators on variable exponent Lebesgue spaces.