Li, Jun Feng, The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators, Acta mathematica Sinica. English series (Print) , 21(6), 2005, pp. 1495-1508
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 < ..