The Commutators Of Hardy-Littlewood Averages Operators

Harmonic analysis originated from the study of heat conduction equations. Through 200 years of development, harmonic analysis has closely relationship with the branch of different subjects. It was widely used in every areas of mathematics, especially in partial differential equations and algebraic number theory.The boundedness of operator and its commutators in every functional space is always a focus in harmonic analysis. We will mainly discuss the boundedness of the commutators of weighted Hardy-Littlewood (H-L) Averages operators and fractional Hardy-Littlewood averages operators on the Herz-type spaces. First of all, we will introduce the background, prepared knowledge and the recent development, this chapter is basically preparing for the following chapters of the thesis.Secondly, we consider the boundedness of commutator of weighted H-L averages operators with BMO functions on Herz-type spaces.Thirdly, we consider the boundedness of commutator of weighted H-L averages operators with Lipschitz functions on Herz-type and Morrey-Herz spaces.Finally, we consider the boundedness of commutator generating by fractional H-L averages operators with Lipschitz functions on Herz-type spaces, as well as high order commutator.