The Boundedness Of Multilinear Integer Operator

In this paper, we study the boundedness of the multilinear integer operators ,i.e., we study the boundedness of multilinear integer operators generated by BMO functions, Osc functions or Lipschitz functions on L^p(1 < p <∞) space,Hardy space,Herz - Hardy space and Triebel - Lizorkin space.At first, the sharp inequalities for the multilinear integer operators gener ated by Osc functions are proved. By using it, we obtain T^A(f) are bounded on L^p(ω)(1 < p <∞) space and weak Llog L space.After that, the boundedness for the multilinear integer operators generated by BMO functions on H_D^mA^p(Rⁿ) space and H(?)_q,D^mA^α,p(Rⁿ) space are proved, where D^m A∈BMO(Rⁿ), |β|=m_i, 1≤i≤l. In fact, it is also bounded on HK_q,D^mA^α,p(Rⁿ) space.Then, we get that the multilinear integer operators generated by Lipschitz functions are bounded from L^P(Rⁿ) to (?)_p^lβ,∞(Rⁿ), where 1 < p <∞, and L^P(Rⁿ) to L^q(Rⁿ), where 1/p - 1/q = lβ/n and 1 < p < lβ/n.