Function Spaces With Variable Exponent And Related Topics

In this dissertation, some function spaces with variable exponents and the bound-edness of some operators are researched. For the function spaces with variable ex-ponents, we introduce some basic properties of Herz spaces with variable exponent. Then we give the definitions of Herz-type Hardy spaces with variable exponent and their atomic characterizations, molecular characterizations, real-variable characteriza-tions and wavelet characterizations. Similarly, we define the local Herz-type Hardy spaces with variable exponent. About the boundedness of some operators, we dis-cuss the boundedness of higher-order commutators of a class of Marcinkiewicz integrals on variable Lebesgue space, Marcinkiewicz integrals and other some operators on the Herz spaces with variable exponent, fractional integrals and other some important op-erators on the Herz-type Hardy spaces with variable exponent and the parametrized Littlewood-Paley operators on the weighted Lebesgue spaces and the weighted Hardy spaces.