Estimation Of Some Operators On Wiener Amalagm Spaces

Function space and operator are the two main research objects of harmonic analysis In this paper,we study the boundedness of singular integral operator,fractional integral operator and a class of sublinear operators on several kinds of Wiener amalgam spaces by means of the classical real analysis method in harmonic analysis.The paper can be divided into three parts as follows:Firstly,the historical background and application value of harmonic analysis are briefly introduced,and then the historical background,development process and current situation of Wiener amalgam spaces,as well as the notation and main structure of the thesis are introduced in detail.In the second section,the definition and historical background of a class of sublinear operators and BMO spaces are introduced.By introducing weighted BMO-type Wiener amalgam spaces,the boundedness of this kind of sublinear operators is obtained.By using similar techniques,the boundedness of this kind of sublinear operators on weak Lp-type Wiener amalgam spaces is proved.In the third section,the definition and historical background of singular integral op-erator,fractional integral operator and non-doubling measure are introduced.The bound-edness of singular integral operator and fractional integral operator is obtained by intro-ducing several kinds of non-doubling measure Wiener amalgam spaces.