Boundedness Of Multilinear Singular Integral Operators With Rough Kernel And Its Commutators On Some Function Spaces

The core of this thesis, which consists of three chapters, mainly studies the boundedness properties of the multilinear singular integral operators with rough kernels and it’s commutators on some function spaces.In the chapter1, under some assumptions about the kernel, we obtain that the multilinear singular integral operators with rough kernels is bounded on the homogeneous Morrey-Herz spaces by using the divide skill of functions and its LP-boundedness.In the chapter2, by using the result of chapter1, the LP-boundedness and BMO function’s properties, we prove that Multilinear commutators T→b is bounded from the spaces MKp1q1α1,λ1(Rn)×MKp2q2α2,λ2(Rn)×…×MKpnqnαn,λn(Rn) to the spaces MKpqα,λ(Rn).In the chapter3, we get that the multilinear commutators T(a→,b→) is bounded on the weight Lebesgue spaces Lωp(Rn) under some assumptions about the kernel K(x,y1,y2...ym) by using the properties of Λp weights and the sharp maximal function estimates.