Dini型多线性Calderón-Zygmund算子在Herz型Hardy空间上的有界性

Boundedness of multilinear Calderón-Zygmund operators of Dini type kernel on Herz type Hardy spaces

为了研究Dini型多线性Calderón-Zygmund算子在Herz型Hardy空间上的有界性,通过对空间进行环状分解,利用中心原子对Herz型Hardy空间进行特征分解,再利用原子的消失性条件得到衰减估计,从而叠加得到结论。证明了当α>n(1-1/q)时,Dini型多线性Calderón-Zygmund算子是从Herz型Hardy空间到Herz空间是有界的。

In order to study the boundedness of Dini-type multilinear Calderón-Zygmund operators on Herz-type Hardy spaces,the space was morphologically decomposed,the Herz-type Hardy space was eigen-decomposed by the central atom,and then the vanishing condition of the atom was used to obtain the attenuation estimate,so as to superimpose the conclusion:when α>n(1-1/q),the Dini type multilinear Calderón-Zygmund operators are bounded from Herz type Hardy spaces to Herz type spaces.