Boundedness Of Operators On Anisotropic Spaces

In this thesis, firstly, the anisotropic Herz-type Hardy spaces and several results of them are introduced. We obtain that the oscillatory singular integral operators are bounded from HKq,?,p(A;Rn) to Kq?,p(A;Rn) with the atomic de-compositions of the spaces. Secondly, we recall the anisotropic weighted Hardy spaces and some basic theories of them. With the atomic decompositions of the spaces and some properties of operators, we prove that the strongly singular in-tegral operators are bounded from HP(A;Rn) to L?p (Rn). And by using the prop-erties of weighted functions, such operators are also bounded from H?p(A;Rn) to H?p(A;Rn). At last, the anisotropic weighted Herz-type Hardy spaces and some basic theories of them have been introduced. By using the inequality estimates and the atomic decompositions of the spaces, the boundedness of the strongly singular integral operators on Hq?,p(A,?1,?2) are obtained.