Weighted Hardy Type Operators And Commutators In The P-Adic Fields

The boundedness of some classical operators and the characterization of the commu-tators for function spaces are the two most important research topics in harmonic analysis.However,Euclidean space as the underlying space has been playing their stages.In recent years,a number of important operators associated with the P-Adic field vector function space classes in harmonic analysis have become another emerging field.Specifically,sharp estimates for the Hardy type operators in the different P-Adic spaces.This article focus on sharp estimates for the Hardy type operators and the boundedness of multilinear commutators in the P-Adic field.The outline of the paper is organized as follow:In chapter 1,the research background,current situation and the structure of the article are introduced.In chapter 2,it is proved that the accurate estimation of the higher-dimensional P-Adic Hardy operator in the P-Adic Lebesgue product spaces.In chapter 3,the sufficient and necessary conditions are established for weighted P-Adic Hardy operator in the P-Adic Lebesgue product spaces.In chapter 4,the sufficient and necessary conditions of weighted multilinear P-Adic Hardy operator are discussed in the P-Adic Morrey spaces.In chapter 5,the boundedness of commutators of the weighted multilinear P-Adic Hardy operator is proved in the P-Adic center Morrey spaces.