Boundedness Of Commutators On Herz Triebel-Lizorkin Spaces With Variable Exponent

The boundedness of commutators of operators and the characterization of function spaces have always been concerned by scholars.So in this paper,lighted by the idea that the boundedness of commutators of operators could characterizes Lipschitz spaces,we obtain the boundedness of commutators of some operators on Herz Triebel-Lizorkin spaces with variable exponent.Its main contents are as follows:In the first chapter,the background and preparation of Herz Triebel-Lizorkin space variable exponent related to this dissertation are introduced.In the second chapter,by using two families of operators,Peetre maximal operators and some definitions and lemmas of Herz Triebel-Lizorkin spaces with variable exponent,the equivalent characterization of the norm for Herz Triebel-Lizorkin space with variable exponent is acquired.In the third chapter,based on the equivalent characterization of Herz Triebel-Lizorkin spaces norm with variable exponent,the boundedness of commutators for sublinear operators on Herz Triebel-Lizorkin spaces with variable exponent is obtained by using the size condition and boundedness of sublinear operators.In the fourth chapter,by using the equivalent characterization of Herz Triebel-Lizorkin space norm with variable exponent,it is established that the Marcinkiewicz integral commutator is bounded on Herz Triebel-Lizorkin spaces with variable exponent when satisfying a weaker Ho rmander condition.