Some Properties Of Commutators Of Singular Integral Operators On Triebel-Lizorkin Spaces

Function space has a long history and has played an important role in the classi-cal and modern mathematics.The continuous space inside the function which study the differentiability and integrability still attracts the attention of scholars,these properties are important for differential equations and partial differential equations with the study of Triebel-Lizorkin.The space in the function space theory plays an important role.As everyone knows,in the research of function space,operators and their commutators of operators on function spaces is essential.This paper mainly studies some properties of commutators of singular integral operators on the Triebel-Lizorkin space,this paper main-ly consists of the following five chapters:In the first chapter,the background of the study,the current research situation at home and abroad and its main results are expounded.In the second chapter,the Lipschits space is portrayed by the boundedness of the linear(or iterative)commutator of the bilinear singular integral operator in the Triebel-Lizorkin space.In the third chapter,we verify a feature of variable exponent Triebel-Lizorkin spaces and obtain some properties of commutators of singular integral operators in variable ex-ponent Triebel-Lizorkin spaces by using this characteristic.In the fourth chapter,we prove that some commutators of operators on Morrey Triebel-Lizorkin space is bounded to characterize Lipschits space,where operators in-cluding Calder'on-Zygmund operator,Riesz operator,Littlewood-Paley operator,the po-tential of Marcinkiewicz integral and Bochner-Riesz operator.In the fifth chapter,we discuss the boundedness of the sublinear operator in Herz Triebel-Lizorkin space when a certain size condition is satisfied.