Abstract
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some Lp(ℝn) to Lq(ℝn) when the m–th order derivatives of A belong to Lr(ℝn) 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 (Lp, Lp)–type operators for 1 < p < ∞.
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