Research On Some Operators And Their Commutators On Mixed Norm Morrey Type Spaces

Since function spaces with mixed norms have a finer structure than the corresponding classical function spaces,they are widely used in partial differential equations.This article first reviews the research background,current situation and main points of this article on mixed-norm function spaces.As a result,the relevant definitions and lemmas are introduced,and then the commutators of singular integral operators(including Calderón-Zygmund singular integral operators and fractional integral operators)are bounded on the mixed-norm Morrey space.In addition,The norm estimation of the fractional integral operator in the index p?n/? is obtained.Finally,two types of mixed Morrey type spaces are introduced,and the weighted norm inequalities of a class of multilinear operators and their commutators on these two types of mixed Morrey type spaces are established.