The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators

In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L p(.n) to L q(.n) when the m.th order derivatives of A belong to L r(.n) for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m.th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are (L p, L p).type operators for 1 < p < ..