Some Properties Of Multilinear Singular Integral Operators

This dissertation is devoted to the boundedness of multilinear singular integral operators. Boundednesses for multilinear singular integral operators with kernels of some weak regularity conditions are obtained on products of Lebesgue spaces. Besides, some multi-weight weak type estimates are established for the multilinear Calderón-Zygmund operators.In the second chapter, some multi-weight estimates for multilinear Calderón-Zygmund operators are established, which is also a generalization of the results constructed by Cruz, SFO and Pérez.In the third chapter, when the associated kernels merely satisfies the H(?)mander type regularity conditions, we obtain boundedness for multilinear singular integral operators on products of Lebesgue spaces, and show the equivalence between the boundedness from L_c~∞(n)×...×L_c~∞(R~n)1 to BMO and the boundedness on spaces. By strengthing the regularity conditions to a kind of L_c~∞(n)×...×L_c~∞(R~n)1ω-type, an endpoint estimate is provided for multilinear singular integral operators. The key tool used in this chapter is John-Str(?)mberg sharp maximal operators.In the final chapter, when the associated kernel satisfies the standard size condition and regularity conditions of H(?)mander type orω-type, boundedness is proved for the corresponding maximal operators of multilinear singular integral operators, and without resorting the boundedness of multilinear singular integral operators themselves. Lp...