Vector-valued Maximal Multilinear Calder(?)n-Zygmund Operators With Non-smooth Kernel On Weighted Morrey Spaces

The theory of multilinear Calder(?)n-Zygmund operators was firstly introduced by R.R.Coifman and Y.Meyer in 1970's.Subsequently,many scholars have done a lot of researchs about Calder(?)n-Zygmund operators,including its weighted boundedness and boundedness of commutators.In this paper,we mainly study the boundedness of vector-valued multilinear Calder(?)n-Zygmund operators with non-smooth kernel on weighted Morrey spaces.Firstly,we introduce the development prospect and primary results of vector-valued multilinear Calder(?)n-Zygmund operators with non-smooth kernel.Sec-ondly,we show the boundedness of vector-valued multilinear Calder(?)n-Zygmund opera-tors and maximal truncated operators with non-smooth kernel Tq,Tq*on weighted Mor-rey spaces.Finally,we obtain that boundedness of vector-valued multilinear Calder(?)n-Zygmund operators and its commutator T?b?,q generated by BMO(Rn)function and max-imal truncated operators and its commutator T*?b,q generated by BMO(Rn)function withnon-smooth kernel on weighted Morrey spaces,respectively.