参数型多线性Marcinkiewicz积分在Campanato空间中的存在性和有界性

Existence and boundedness of parametrized multilinear Marcinkiewicz integral on Campanato spaces

该文研究了带Lipschitz核条件的参数型多线性Marcinkiewicz积分μρ在Campanato空间中的存在性和有界性.具体而言,一方面证明了若μρ在某一点有限,则几乎处处有限;另一方面建立了μρ在Campanato空间中的范数不等式.

In this paper,we study the boundedness of parametrized multilinear Marcinkiewicz integralμρwith Lipschitz kernel on Campanato spaces.We show that if the operatorμρis finite for one point,then it is finite almost everywhere.What's more,norm inequalities are established on the corresponding Campanato spaces.